It is possible to still apply for citizenship with misdemeanors on your record; however, there are so many unanswered questions that need to be answered to determine the best course for you. For example, you were charged, but did you plead guilty, get convicted, cases dismissed etc? What were the charges? Also, and more importantly, I assume you were born in another country, but how did you arrive in the U.S., what are your connections, etc.? That really is an essential part of your question, and something you should run by an attorney face to face.