Just to clear it up: the preferred translation is "El martes voy a comer pollo." But "voy a tomar" is correct, too. Just like drinking something can be expressed with tomar, so can eating something.
The a here belongs to the construction "ir a" which is the Spanish equivalent of the English "going to".
There is one thing wrong with it. :)
The construction "ir a [verb]" is pretty much what "going to" is in English and has rarely something to do with actual moving. Rather, it's an expression to describe the immediate and/or planned future.
Your sentence could be translated as "El martes me voy para comer pollo." - "On Tuesday I go (in order) to eat chicken."
You need to know two things - which person (or thing) is doing something in the clause, and how many verbs are in the clause.
You should already know that first item - it depends on whether the person doing something (the subject of the sentence) is the speaker themself (I, yo), the listener (you, tú) or someone or something else (he/she/it, él/ella); or a group including the speaker (we, nosotros/-as), including the listener (you, vosotros/-as), or none of them (they, ellos/ellas).
Depending on that, each verb gets various suffixes indicating who does the thing, and since those suffixes are unambiguous most of the time, you can generally leave out the subject pronoun. For the verb comer it looks like this:
- yo como
- tú comes
- él/ella/usted come
- nosotros/-as comemos
- vosotros/-as coméis
- ellos/ellas/ustedes comen
Now the second item is important in this sentence. If you have multiple verbs in a clause (for instance a modal verb like "can", "must", "should", and a full verb), only the first verb is conjugated - the rest stays in its infinitive form. That's why you got "voy a comer" here: voy is the yo-form of the verb ir, and comer stays unchanged. Like in English: I am (conjugated) going (participle) to eat (infinitive).