truck sways on highway

have a 1999 blazer 4 door 4x4 when i get up to highway speed about 60 mph it sways. could it be cause the back tires are brand new and the front tires are pretty worn. I tried to get an alignment done a few months ago but they said they couldnt do it cause there was too much play in the pitman arm. Could that have something to do with the swaying?

Yes.
Sounds like time to get it fixed and have a look at other front end parts.
Tie rod ,ball joints, idler arm and bushings,wheel bearings and shocks.
Good luck
MT