My honest advice would be don't explain it. In truth justifying a tractor beam existing with hard science is very hard, and further more any technology that makes it possible would likely have other uses, meaning you would then have to expand your world to include all the other technologies that would invariably come from the first.
However, one of the cool things about science fiction is you get a certain free reign to say 'scientists invented it and it works like X', and so long as you don't violate any obvious hard constants of the world, most noticably in this case conservation of energy, you get allot of leaway to say it works because of principles that we just haven't discovered and trust me on this, so long as you set clear rules and stay consistent to them.
Trying to justify the science with hard facts is something I don't suggest trying unless you have very strong physics skill, because otherwise your likely to get part of the science wrong when explaining the technology and end up with a situation where the obvious flaws with the science just make it more obvious that the technology doesn't make sense
However, that's writing advice, not world building advice so moving on...
If you want to justify this the best explination I can suggest is gravity manipulation. Some method of shaping gravity was created such that you can create a strong gravity field which projects outwards from your ship, making objects 'fall' towards you. This works much better if your tractor beam can only pull, not push, objects, though with only a bit softer science you could probably handwave by saing you can manipulate gravity enough to create limited pushing effect.
This works best because it's drawing on a basic force of nature which already does what you want, and gravitons and gravity in general still is not entirely understood on a full quantum level, making it at least mildly possible that creating of gravitons may be somehow possible. Though already my mind is throwing up questions as to how this would work that I don't think about if someone just says "we have a tractor beam" without justifying it as gravity. In short this is the best answer I can think of, but I still advice against not giving any.
If you do have the ability to manipulate gravity you know have short range weapons to crush ships, potentially shields to deflect projectiles (depending on how much control you have of gravity), anti gravity ships that can 'float' at high speeds through the air of any planet, and of course artificial gravity for your ships, to name but a few related technologies that come from this. To minimize the questions people ask I would suggest saying that gravity is created only through a process like nuclear annihilation, or that you can only shape gravity but not create it, to justify the fact that only massive ships can manipulate gravity, to avoid question as to why small scale gravity manipulation isn't used for technology X.
Also keep in mind that whatever technology you create your need to abide by conservation of energy. Moving anything large, like an astroid, in space means applying a massive force to it, which in turn means a massive energy expenditure. Your want to think about just how much energy your spending to move objects, and rather the ship engaging the tractor beam has that much energy readily available to expend (suggesting an order of magnitude more energy then the tractor beam used is available to it). It's easily possible to explain that ships do have that much energy available, but keep in mind just how massive energy that is and what someone can do with that much stored power. Any ship with that much power is capable of being quite lethal to anything around it if it transfers enough energy rapidly enough, just for starters.