Yes it is possible. Take Mercury, for example.
'It takes Mercury about 59 Earth days to spin once on its axis (the rotation period), and about 88 Earth days to complete one orbit about the Sun. However, the length of the day on Mercury (sunrise to sunrise) is 176 Earth days.'
Tides are not just created by moons, but by the sun. The closer to the sun, the stronger the tidal effects. The shallower the water, the greater the tidal effects. The slower the planet spins, the longer the 'day' and the solar tide. The lower the gravity of the planet, the greater the gravitational effect of the sun on the water. The length of the solar day determines the length of a solar tidal cycle.
However, it depends on what you mean by a 'day'. A solar day and a solar tide would have to coincide.
Or your world could be a moon around a massive planet, which creates a 'moon tide' on the moon itself. Thus, the moon tide and the solar day do not have to coincide.
The further away the moon is from the planet, the longer it takes to make one revolution. The length of the moon tidal period would be a combination of the rotation of the moon around itself, and the rotation of the moon around the planet. The length of a solar day on the moon would be determined by the rotation of the moon around its axis, and the rotation of the moon-planet combination around the sun. Eclipses would be a factor.
On Earth, the time of a moon tide and its strength is determined by the Earth's rotation around its own axis, and the period of the rotation of the Moon around the Earth. See the referenced article for an example of how this can be calculated for the Sun-Mercury combination.
You can do all of the calculations if your readership is absolutely demanding, or you can just assume the parameters are correct on your world for a non-discriminating readership. For a short story, assume. For a space opera, calculating it is perhaps the preferred method.
However to be science-based, your calculations would have to include an analysis of the tendency of the moon-planet combination to be tidally locked.