You may wish to search the national websites of the sororities at your school. For example:
http://www.sigmakappa.org/Scholarship_Policies/ If your chapters are smaller, there are fewer ladies to balance out your 2.26 and there is a required overall chapter standard. They have to follow National procedures, so here is a way for you to research outside of what you already know we'll say.
I agree with the other posters. When you search, you'll see that Nationals
MAY ALLOW a lowish GPA, but that is the lowest standard allowed. (It may not matter to your school, but as an example, you are below their eligibility to pledge.) The info you could research would give you the absolute lowest that Nationals will allow, but there is a lot of pride in having the highest grades, scholarship awards, etc... that encourage chapters to want high grades from their PNMs. Secondly, grades can affect whole chapter rights/opportunities. Because of this, bringing in a woman with a quite low GPA knowing that several sisters would have to have much higher grades to balance it out doesn't work in your favor either. But being below even the lowest required GPA makes all this moot.