If the alignment is not changing, that's called "torque steer". Control arm bushings are the most common cause of that but a really sloppy strut, as in one that's been making noise for a long time, can cause that. The most common cause is a tire pull. The clue can only be found on front-wheel-drive cars because you need to be able to make them pull during acceleration. The car pulls one way when accelerating and the other way when braking. To prove it's the tires, switch them side-to-side. It will either pull the other way when accelerating or there's a small chance the car will go straight. You can also rotate the tires from front-to-back but I've been fooled more than once by having a similar pull with the rear ones I put on the front.
If switching the two front tires identifies them as the cause, THEN you can switch them to the rear. If the car goes straight, just leave them there until they're worn out and must be replaced. It's fairly common to get a pull from a difference in how the tread and sidewalls squirm and flex. That in itself is not an indication a belt is about to break or some other failure will occur. New tires can cause a similar pull. In fact, I had a real hard pull many years ago with brand new tires. Moved the right front to the rear and got over 45,000 miles out of them.