Is there a single word to mean the process of making someone angry by calling him angry?

This is a self-fulfilling prophecy.

In a self-fulfilling prophecy an individual’s expectations about another person or entity eventually result in the other person or entity acting in ways that confirm the expectations.

The term is sometimes over-generalized to many other situations, but the definition clearly indicates the situation presented here.

Britanica

Exasperate seems to fit the bill quite nicely.

To exasperate someone is to annoy him or her to the point of impatience, frustration and irritation, like when you exasperate a busy waiter by asking questions like "what are all the ingredients in the salad dressing?" and making him repeat the specials five times.

[Vocabulary.com]

In a broader sense, (inclusive of the specific scenario) the words instigate and provoke can be used to accurately describe this behavior. Both can be used to describe the act of eliciting a negative response.

"I was in a good mood until Bob provoked me to anger."

"Mary is a troublemaker -- she likes to instigate arguments, by spreading gossip."

I think, "to anger" suits.

According to Merriam-Webster's Dictionary https://www.merriam-webster.com/dictionary/anger:

anger

transitive verb

: to make (someone) angry

// He was angered  by the decision

Baiting:

bait verb [ T ] (MAKE ANGRY) ​

to intentionally make a person angry by saying or doing things to annoy them: