Squidward is usually the character drinking tea, in several episodes.
In the episode "Not Normal," SpongeBob goes over to Squidward's house to drink some tea.
No tea is actually drunk in "Tea at the Treedome" until the very end where Sandy puts the teabags in SpongeBob and Patrick's new water helmets, which turns the water into tea.
In "Grooming Gary," while SpongeBob is checking Gary's "Slime Viscosity," he runs through Squidward's house, who is sipping tea.
In "House Fancy", Squidward drinks tea at the beginning of the episode, and spills it when he's shocked at the sight of Squilliam appearing the show, House Fancy. He later refers to it as the "hideous stain on the rug".