Depends on what you mean with "equivalent".
In meaning, yes, but in style, I'd say no -- the German comes across as a lot more archaic to me than the English.
It'd be fine in a period drama set in the Middle Ages but from anybody born in the last 100 years it's likely to come across as comical, I think. Not merely humorous as "methinks" might.
I wouldn't even be surprised if there were a fair number of people who don't know that word.
(I'm not even sure what the difference is between mich dünkt and mich deucht. ...search... Ah, apparently, deuchte was the old irregular past tense but deucht is now sometimes used as an alternative in the present tense.)
http://retropedia.de/Wortgeschichte.12.0.html?&cHash=6509b47ec8ae0db93df9d2992c553425&tx_ttnews%5BbackPid%5D=35&tx_ttnews%5Bswords%5D=Frau&tx_ttnews%5Btt_news%5D=896 has an interesting comment on using it in a non-poetical context, with something as prosaic as "our colleague seems to be having an extended lunch break again today", to add a kind of verbal wink.
So... it's tricky. Denotation pretty much the same, connotation / pragmatics not so much.