It should read:

I'll be taking an English exam in a couple of weeks, so I need to practice.

or

I am taking an English exam in a couple of weeks, so I need to practice.

or

I take an English exam in a couple of weeks, so I need to practice.

You use the "to be" verb usually in conjunction with another verb (as here with "be taking"). I'll breaks down to "I will" and will is an auxillary verb.

"I am taking" can be used as a simple form of future tense "am" verb. "I take" is also a way to use simple form of the future tense.