Our DM has a rule that if your Strength modifier is -1 or lower, drawing your weapon is a full-round action. If you have a neutral or positive strength modifier, drawing your weapon would become a quick action. However, none of the research I have done supports this. Is this an actual rule, and (if so) where could I find it?
The particular rule you've given is a house rule. Strength does not affect a character's ability to draw their weapon. However, the rules for drawing or sheathing a weapon state,
If you have a base attack bonus of +1 or higher, you may draw a weapon as a free action combined with a regular move.
Therefore, characters with a BAB of 0 would have to spend a move action to draw their weapon. Characters with a BAB higher than 0 can take a free action to draw a weapon as long as they also take a regular movement action that round.