The former Los Angeles-dwelling popstar is said to regularly visit the club near his Wiltshire mansion for games of five-card stud with Jonathan Wilkes, The Sun reports.
A source said: "Robbie has been in frequently over the last few weeks. He plays to a very high standard and has been having fun with Jonathan.
"He's getting a reputation as a serious adversary around the poker tables here."
Reports recently emerged that Williams's relationship with actress Ayda Field is "stronger than ever", despite his return to the UK.