Most emphatically NO! The point of a mixer is for a sorority and fraternity to spend time getting to know each other. The only people allowed to be in attendance are the members of that sorority and that fraternity. If you brought a date, your sorority could get an infraction, which means they might have to pay a fine or be placed on social probation.

Sorry if I seem a little strong, but it really worries me that your new sisters (I assume you are pledging this semester) haven't told you basic things like this.