Yes, will is a verb, specifically a modal auxiliary, one of the helper verbs like can and might that add meaning to a main verb.
She will call tomorrow. Here will helps the main verb call, so the whole phrase works as the verb.
I will get an A in this class. Here will shows intention, a plan the speaker is already set on. The verb it helps, get, carries the action; will just adds the attitude.
Will you buy me some chocolate? Here will turns the sentence into a polite request for a favor, softening the ask while still pointing to something not yet done.
The mix-up to avoid is with the noun will, which is a different word despite the same spelling. As a noun, will names a thing: a legal document (she signed her will) or determination (free will). Those are never verbs.
A quick test: if a determiner like a or the, or a possessive like her, sits in front of will, it is the noun (a strong will, her will). The modal helper never takes one in front of it. In Her will was to travel, the possessive her signals the noun, even though a verb follows.