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It could be a number of things. Wheels not balanced properly. Loose or missing lug nuts. Bad bearings. Bad or missing suspension bushings. Broken shock absorber on one side. Could be a bad tire or even a bad leaf. Does it happen on flat pavement or bumpy/washboard roads? Does it only happen at highway speeds? Is the issue random or can you reproduce it? Can you please provide as many details as possible. Also, just curious, how are you certain its not an alignment issue?
Ya until you get it checked alignment can cause that, specifically a lack of caster will cause you to wander all over the road. Consider 6°+ the minimum you want.
But the most likely culprit/s are worn steering parts. So do the standard checks tie rods, drag link, ball joints. Then check the steering box for play and finally the rag and slip joint in the steering column for play/wear.
Then check for worn suspension parts, bushings specifically I-beam and leaf spring, if either of your TTBs are moving around, you and the truck will be too.
And of course, wheel bearings make sure there is no play in them.
If all of that checks out then it is a caster issue
Not enough toe in. Measure the distance in front of your tires from tread outside edge to tread outside edge. Then do the same at the backside of the tires. You should have slightly less on the front measurement (like maybe 1/4"-3/8"). Also before you take the measurement, drive foreword about 10 or 20 feet in a straight line and come to a stop slowly. Then the truck will sit as close to a driving stance as possible. If you don't have enough 'tow in' (front measurement shorter than the back) then your truck will wander like that. If you have too much, you will find it cutting sharper than you want into turns, and you'll feel the front suspension climbing up on sharp turns. .
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