In Tangerine, Victor says to Paul, “If you’re a War Eagle, then you're a War Eagle.” What does Victor mean in that paragraph?

In that sentence and throughout that paragraph, Victor means that membership on the team means membership in a group of fiercely protective friends.

... "But I saw you playing hard out there, too. And I saw you get a piece of that fullback." "Listen, Fisher Man, here it is. If you're gonna play with us, then you're gonna play with us. Do you understand?" ... "If you're a War Eagle, then you're a War Eagle. You got brothers to back you up. Nobody's gonna mess with you, not anyplace, not anytime. Do you know what I'm sayin'?"

Although Victor's words leave Paul somewhat in a daze, Paul definitely understands what his new friend is saying, here at the very end of the chapter titled "Friday, September 22."

What Victor means is that, first, Paul played well in the soccer game. He proved himself worthy of being on the team. And because he really belongs on the team now, Paul has earned himself the friendship and loyalty of all the team members. That is, they will protect him in any situation: on the field or off the field, at school or anywhere. Like a family, or a gang or the Mafia if you prefer, the members of the War Eagles soccer team look out for each other and stick together as a unit.

This assurance means a lot to Paul, who has rarely had more than a few friends at a time, and who constantly deals with the rough, menacing nature of not just his peers at school but also his vicious older brother.