Can I still get a US visa or become a citizen if my dad is a military deserter?

Generally, if a foreign national otherwise qualifies for immigration benefits, the wrongful conduct of his/her parent will be irrelevant. Of course, there are many other details that determine eligibility for immigration benefits. It would be wise for you to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.