I have an idea that the seas of a world are red, not blue. However, the world should also be the birthplace of an intelligent alien species. Would it be scientifically possible to have a world with a red sea and where intelligent life can still develop?
Absolutely. There's actually a sea on Earth which is red(ish).
So it wouldn't take that much extrapolation to extend the algae planetwide and make it a brighter color. I'd think you'd want it to be loosely matted enough to provide flow of oxygen and sunlight, but that shouldn't be too hard to finesse.
I decided to delete my comment and answer the question.
Here's your problem:
This is a chart of color absorption for water. It shows that blue is reflected very well (water doesn't absorb blue). On the otherhand, it absorbs red very well (no reflection). It's exactly the opposite of what you want. But...
You can shift the solar color from yellow to red. This means less blue spectrum is transmitted to your world and more red. This would help (although the seas may appear more yellow than red), but they would appear dark since most of the red wavelengths are being absorbed. But, it's a blank canvas. This is really important.
We need your sun to pump out more ultraviolet. This means your aliens will be very naturally resistant to sunburns on other planets because they would have evolved natural UV protection. Why do we want this?
Because Chlorophyll glows red under ultraviolet light.
BUT! As with all things, you can't simply play with the dials on your planet without consquences. Many things glow under UV (a black light) and they'll be happily glowing, too. I've already mentioned the need to give your aliens natural UV protection. And playing with the sun's color means playing with the nature of vegitation. Can you get your intelligent aliens? Sure!
But it also means you need to pay attention to the details of what else will be affected by whatever solution you choose to make your seas red. For instance, the price you pay to get glowing chlorophyll is that you may not have it since your plants may need to find a way to thrive in a UV/Red predominant energy source. Whatever you choose, take the time to think through "what can go wrong with this?" It'll actually add a lot of cool interest to your story. ("What do you mean you can't eat lettuce? It's the most neutral plant on our planet!")
Sure. Just have a microorganism endemic to the seas that colours them red. Some sort of algae, maybe, that produces a red dye naturally as part of their life cycle. We kind of have that here on earth, manifesting as a red tide during algal blooms.
If the coloration is produced as part of the normal behaviour of the algae, rather than during oxygen-consuming blooms, you're good to go.
If the oceans contain very high concentrations of iron, in the form of rust, it would create a red ocean.
This environment would be ideal for rust-eating microbes, which could form the base of oceanic food web in the same way photosynthetic plankton form the basis of our aquatic food webs.
What implications this has on your world's plant and animal life is outside the reach of my familiarity with biology, but I don't think it would necessarily preclude the development of intelligent lifeforms.
If you want a really exotic answer, perhaps your world has a Fluorescein ocean. Fluorescein is in essence a complex carbohydrate, or in other words an organic compound, that naturally 'red-shifts' light, absorbing photons and releasing longer wavelength, lower energy photons as a result.
It typically exists as a powder, but can be dissolved in water or alcohol, though not all that well. BUT - imagine if you will a world in which your oceans first formed with a lot of this compound in them, and your first underwater plants used photosynthesis to break down this compound, producing just enough oxygen for their needs. They couldn't release excess oxygen as this would wreak havoc with the fluorescein, but let's just say that they could metabolise the fluorescein via an endothermic reaction triggered by sunlight (or some other energy source).
Because it's in solution, it's not that hard to evolve out photosynthesising animals that metabolise the fluorescein more effectively through being mobile, and potentially even evolve predation (although there would be less need for that in this environment because your organisms have evolved in soup).
The catch with this is that you are unlikely to have a great oxygenation event, and therefore far less likely to have land based creatures, but it's possible you could develop intelligent life in a fluorescein ocean, breathing their food and oxygen supply straight out of the water.
Your Ocean has a high hemoglobin content
I would suggest using some sort of symbiotic system where said ocean thermally convects hemoglobin to the surface where it absorbs Oxygen from the atmosphere. This would create a bright red color. The convection along with the weight of the molecule could then cause it to sink where a certain organisms in or on the bottom of the sea deplete the Oxygen where it will gradually turn a darker shade of red, at which time it will convect upward beginning the cycle again. An aquatic marine animal which has hemoglobin based blood and a special gland for absorbing the molecules would work. Perhaps the 'bloodfish' is responsible for, or a result of this entire ecoaquatic system.
There are two easy ways:
The color "blue" is partially a function of light reflected by the sky. If the sky is red to the human eye, say due to dust, the water will be reddish.
On Earth, Chlorophyll (the green component of plants) actually reflects more red light than green. Our eyes are more sensitive to the green light than the red, so it appears green to our eyes. Plants that have slightly different chlorophyll or higher proportions of other pigments, such as the algae that @jdunlop mentions, do appear red to the human eye.
Edit In spite of my memory, chlorophyll does not reflect more red than green, even when fluorescence is allowed for. The only way this makes sense with plant pigments is with carotenes or other red pigments.
The reason our own ocean is blue is because of the color of the sky. If your sky is red/orange, you might end up with a red ocean. You could also do what a couple others have said and try an alga that's red.