The cause of a Dodge truck pulling to the right has many possibilities. Tires are the most common problem. An uneven tread pattern or separated tire tread will always cause a strong pull. The tire tread need not be separated at an unsafe level --- a mild separation where the tread had comes loose inside the tire at one spot --- can lead to pulling. A dragging brake caliper or an out of alignment situation will definitely cause pull.
Loosen --- but do not remove --- the lug nuts on the two front wheels. Place the floor jack under the truck and raise it enough to place jack stands under the frame. Lower the truck onto the jack stands.
Stand directly in front of the tires and rotate by hand while watching the tread closely for uniformity. If at one point the tread seems to wobble, it is slightly separated. Remember this tire's location in the event it becomes a problem later. Do the same for the other tire. If both tires have a wobble or separated tread they should be replaced. Check both sides of the tire's sidewalls for lumps indicating a separated sidewall. If any are found the tire should be replaced.
Remove the lug nuts and the wheels. Swap the wheels from one side to the other and reinstall them. Tighten the lug nuts. Test drive the truck and see if the pulling problem has been eliminated. If it is, now you can be assured it was a tire issue. If the pull is still there, spin the tires and make sure the brake is not binding. If one of the brake calipers is hanging up, remove the tires again then remove the two slider-bolts in the calipers using a socket wrench. Check the slider bolts for lubrication. If there is no lubricant on the bolts or they are corroded, clean them and lubricate them lightly with grease. Reinstall them and rotate the rotor by hand to see if they are still locking up.
If the vehicle is still pulling, take it to a service facility to have the front end aligned.
