Simply, no external forces are strong enough to produce any visible tilt.
What kind of tilt is it?
Why would anything have to tilt?
If the sun had the gravity force, humans bodies would be attracted by such force and then getting tilted/imballanced, even getting sucked by supposedly the sun's huge gravity force.
The Sun is very massive, but also very far away. It's not going to suck us off the surface of the Earth which is less massive than the sun, but we are also very close to it. Standing on it in fact. Think of it like magnets. You can have a huge magnet and a tiny one, which will attract a paper clip? Well if the huge magnet is a mile away and the small one is an inch from the paperclip, which will win? And that huge magnet won't pull every metal object for miles around, it gets weaker the further away it is, just like gravity.
But more importantly, the Earth is in orbit around the Sun. An object in an orbit doesn't feel a 'pull' from the object it's orbiting, it's in free-fall and experiences no pull or tilt.