No, you have to go to that players stat page and click on the button with a plus on the top right corner

In some instances some players, like myself, would rather wait for a few days before joining an alliance (e.g. tutorial game, 39 historical map, etc.).

The only exception for me so far is my first Endgame 1944 scenario, where I chose country at random and find myself fighting as German Army Group Center- allied automatically with German Army Group West and German Army Group South. The nine countries (3 Western Allies, 3 German groups, and 3 Russian fronts) seemed balanced compared to the 39 historical map. I'm in day 2, and I'm already at war with the Belorussian front, who was aggressively patrolling air units- including a bomber- over one of my most populous cities ...

The one on the right. The moment you press, invite will be sent. Go to callofwar.com alliance homepage and you will see it at the bottom where you can revoke it.