Can the judge mail you a court date that would lead to a warrant for your arrest a month after the citation was issued?

Most likely it was not the judge that mailed you the notice to appear in court over the event that you have written about but rather a clerk of the court did the mailing.

If you were subsequently arrested a second time due to your failure to appear in court where notice was mailed to you but you never received it, you will need to explain to the court that you never received the mailing and when you were released from jail the first time there was no court date set for you.

I suggest that given the circumstances that you are now in that you should consult with a criminal defense attorney regarding how to resolve the initial charge and the bench warrant resulting in your arrest for failing to appear at a court date.