Yes; you can transport cigarettes in your UA carryon hand luggage to/from the US. You can also transport cigarettes in your checked luggage. Either way.
You must declare the number of cigarettes you are bringing into the US. The first 200 are duty free, and you then pay duties on the amount over 200 sticks. FWIW a carton of cigarettes contains 200 sticks (10 packs x 20) so one carton is allowed to be imported duty free.
And do claim all quantities you bring in. Not worth the consequences for not complying.
SL