I am drinking tea
is a perfectly acceptable and grammatical sentence. Tea is a beverage, you drink it. It is moreover very common to have a tea break mid-morning. You could have also said,
I am having a cup of tea
Which sounds awfully British, and quite refined.
If instead you have renounced the ancient art of brewing loose tea in a teapot and like me are now dropping white tea bags in a chipped mug, filled with freshly boiled water and waiting exactly one minute before fishing it out with your teaspoon, then say:
I'm having some tea.
If you say this before 4 p.m people will understand the beverage. If you say this from 4 p.m and onwards some might think you are having a light meal, indulging yourself with Devon scones and lashings of clotted cream and jam. But only a few people. People rarely do that sort of thing at home nowadays, it's more likely a couple of rich tea biscuits, or if you're lucky, chocolate digestives. Mmmm....