Yes, it’s possible to join corporations like that. I just don’t remember how when it comes to npc corporations. But when it comes to player corporations you can find them here on the forum under the Corporations & AlliancesRecruitment Center tags. Or you can try to find them in-game through the recruitment channels.
But i can give you an option directly since i am looking after my first pirate.
Have a look there and see if you would like to join this or not.