Inspired by the comments to my answer about (pseudo) 2nd Bar Mitzvahs.
ונער בר מצוה באותו שבת אם יש לו עירנית דוחה לכל החיובים כיון שהוא יום חינוכו
From that I understand that since it's his first chance to get an Aliya, he should be given precedence over (almost) all other people.
Following that logic it would seem that a Ger Tzedek should also be given precedence for an Aliya laTorah immediately after his conversion.
However, I cannot find a source to back up that claim.
Anybody know of a source, or else, a reason why the Ger doesn't deserve preferential treatment?