Question

No, it's not okay. If you are married, you cannot file as single. You have to file as either married filing jointly, together with your spouse, or as married filing separately. If you file jointly, in most cases it would not be legal for your parents to claim you as a dependent.

You seem to be saying that your parents don't know you are married. It's going to be hard to keep that secret for very long, but that's not a tax problem and I can't advise you about how to handle it. They won't necessarily find out because of your tax return, but they might, or it might come out some other way.

You haven't provided anywhere near enough details to determine whether your parents can still claim you as a dependent, but it's rare that a married person can be claimed by his or her parents. One thing that's certain, though, is that if your father is filing your tax return showing you as single, that's not a valid tax return. So your tax return is definitely wrong, and your parents' tax return might be wrong.

when did you get married?  if 2019, then what he did for 2018 is probably okay  (assuming you meet the definition as a qualifying child or relative).   on the other hand if prior to 2019, he's gonna to have a big problem as will you.   You state your father filed for you.  Did you also file your own return?   Did your spouse have income?   if so, how did she file if at all?  

If you were married as of December 31, 2018, and your Dad filed your 2018 tax return using "Single" as your filing status, then you'll need to file an amended 2018 return  (IRS Form 1040X) on which you change your filing status to either Married Filing Joint or Married Filing Separately (the choice would be up to you and your spouse).