Logically a secretive order of vampires shouldn't just take any yahoo off the street.
But they'll take a vampire hunter stupid enough to waltz in with the leader's daughter? And they seem fine with letting random npcs join as "spies" why not you? Here's an easy way to make it make sense:
Vampire hear's about the castle, finds it thinking he'll get in. Volkihar cast a spell on you that makes you black out. Wake up in torture room being interrogated. You say you want to join. They laugh and send you on some suicide mission. You come back and they're impressed. The story goes on from there.
OR
Remember when you go on the quests to turn people into vamp spies? If you ask the questgiver why this perspn was chosen, he'll say it has to do with their blood and the "stars". So basically they think some people are born worthy of joining? Maybe they find out you're on this spiritual list?
See? I made two mediocre solutions in less than 5 minutes. I'm sure the devs could have though of a better one in the time they had.