"It's December now, and today is the eleventh." That's the most natural phrasing. "Today is eleventh" is wrong. There are many ways to say it that are correct, but less natural. I don't want to confuse you by listing them.

You do need 'the', but you don't need 'day': It's the eleventh or It's the eleventh day

Hi! You can say it both ways! You can say, “today is the eleventh” or you can say, “today is the eleventh day of the month.”