Will size 35X12.50R15 tires fit in a 89 F150 with stock suspension

 

No.

Maybe 33's will "fit" but they will still rub at least the radius arms at full lock.

 

35's would fit on but you won't be able to turn your wheels. You'd need a minimum 4" lift, better if it was 6". And you'll probably still rub on the radius arms, but at least the tires won't be hitting the front bumper.
So as BLDtruth said; no.

 

I hope you have at least a 3.73 rear gear ratio.