"Do you have a Weibo account?"
Literally: Do you have Weibo?
We don't usually ask our friends if they have Facebook accounts in English. Do you have Facebook? …will suffice.
There's nothing at all strange with asking someone if they have a "Facebook account" in English.
It should be possible to explicitly use the word "account"; "你有微博賬戶嗎？" (with the traditional Chinese word for "account") and "你有微博帳戶嗎？" (with a traditional Chinese variant word for "account") are both rejected.