We eat tea.. Yaa that's modern Bangla/Bengali.. :)
I drink tea should be correctly said as Ami chaa paan kori. আমি চা পান করি.
But in Bengali we have stopped using the verb drink and we just use the word to eat in place of drink as well.
So, we just say,
I eat tea = Ami chaa khai = আমি চা খাই