The account invites users of the social media site to guess from cropped photographs of people in explicit poses whether those pictured have male or female genitalia.
A series of tweets posted from Huth's official account shows the 30-year-old German apparently playing the game.
Stoke declined to comment on the matter when contacted by Press Association Sport on Friday.
Huth has already faced criticism from within the trans community.
He may face action from the Football Association, who in October handed QPR defender Rio Ferdinand a three-match suspension, as well as a Â£25,000 fine, for comments he made on Twitter.
Ferdinand directed a jibe at a Twitter follower containing the word 'sket', which was understood to be a slang term taken to mean a promiscuous girl or woman.
In their statement concerning the former England captain, the FA said Ferdinand's comment had been "abusive and/or indecent and/or insulting and/or improper" and an aggravated breach as it "included a reference to gender".
One Twitter user, @queenthingy, wrote: " It is clear that @stokecity cannot allow @robert_huth to continue his transphobic adventures
Club being put into disrepute."
Another, @infuriousbeauty, stated: "People might want to consider asking @stokecity football club why their player @robert_huth thinks it's okay to bully trans people online."
Source : PA