Is the word "bring" a linking verb?

No, it's an action verb. It's something someone DOES.

http://grammar.ccc.commnet.edu/grammar/verbs.htm#linking

action verb

The word "bring" is not a linking verb. Linking verbs, also known as copulas, are verbs that connect the subject of a sentence to a subject complement, which provides additional information about the subject. Examples of linking verbs include "be," "seem," "become," and "appear."

On the other hand, "bring" is a transitive verb, which means it requires a direct object to complete its meaning. It indicates an action of carrying or moving something or someone from one place to another. To determine whether a verb is a linking verb or not, you can observe if it connects the subject with a subject complement or if it requires a direct object to complete its meaning.