YOU SAID:
Would you like to join me for a cup of tea?
INTO JAPANESE
一緒にお茶しませんか?
BACK INTO ENGLISH
Would you like to have some tea with me?
INTO JAPANESE
私と一緒にお茶を飲みませんか?
BACK INTO ENGLISH
Would you like to have some tea with me?
That didn't even make that much sense in English.