I am a senior in civil engineering at Clemson and a proud and very active member of my sorority. I know at least for me, it was a bit difficult my first year because I had to spend so much time going to homework help sessions and sometimes they would conflict with sorority new member meetings or chapter meetings, but when it comes down to it, you're at college to get an education, and if there's a conflict between your school stuff and sorority stuff, school stuff comes first. Your sorority will excuse you from mandatory events if you have a huge project or something to be doing for your major.
I know for me, being in a sorority adds another dimension to my college career--it's a perfect compliment to (mostly) all guy classes to have a network of sisters who are there for you, even if you won't see many of them in your classes. Many of your sisters will be dating the boys in your major, and you may be surprised how many of your classmates you find at social events!
I struggled for a short time with whether or not I should wear letters to my engineering classes, because I didn't want my professors to think differently of me. But I've found that I can be a great student while wearing letters, and what is better PR for your organization than to succeed in school and prove any stereotypes of "dumb sorority girls" wrong?
Definitely go through recruitment. You CAN do both a sorority and a difficult major. I've seen countless women do both and excel.

Good luck!