Can I still apply for my citizenship or are there any chances that I can be deported after a battery charge?

Charge is not a conviction; if the charges were dropped, USCIS cannot be use them as basis for deportation. That's the law. Nevertheless, at minimum, you will be given a hard time answering all sorts of questions about that episode. Chances are that USCIS will claim that, even though you were not convicted, your arrest record puts in question your "good moral character". Since only the events of the 10 years immediately preceding the date of the application are considered, you might want to postpone filing your naturalization application until after the 10th anniversary of the date when the charges against you were dropped.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. If the case was dismissed without you having plead guilty prior to the dismissal, you should be fine. However, if you went through a diversion program prior to the dismissal, you may have a problem. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options. Be sure to bring copies of any documents pertaining to you case, including the docket sheet, any minute order evidencing the dismissal, etc.

If the charge was dismissed by the court, then you should be fine to apply for your citizenship. However, if you are not sure about the actual court disposition in your case, you should probably contact an immigration attorney, because battery against a household member would a charge for "domestic violence", which is a deportable crime. In your case, you should probably consult an attorney before you file your citizenship application.

Should be ok if there is the only issue.