Be careful - if you try too hard to change her opinions, she might decide Sci-Fi is no good at all. Try to cater to what you know about her interests.
The Scott Westerfeld "Uglies/Pretties" series might be a good introductory book for a girl who isn't interested in sci-fi yet. It has some interesting dystopian implications, but doesn't obviously have the "ALIENS! SPACE!" aesthetic overtones of most sci-fi, which is what turned me off from sci-fi books as a kid.
(I was also mostly into YA fantasy, and didn't like sci-fi until I discovered the part of it that was really about philosophical and ethical questions, not just aliens and space.)
I hated "Uglies" enough to demand that the audiobook be stopped partway through on a family car trip, but the general idea might be sound. Glancing at my shelf, sci-fi that might work includes:
Archangel series by Sharon Shinn (has a strongly fantasy aesthetic, but is technically sci-fi; the same author does some of both in other series/standalones)
The Host by Stephenie Meyer (especially if this girl likes Twilight, but it might not be young-audience-aimed enough; if you're giving her Ender's Game and its sequels, maybe it's fine)
Tripods series (...
I bought my niece a Kindle that just arrived and I'm about to load it up with books to give it to her tomorrow for her birthday. I've decided to be a sneaky uncle and include good books that can teach better abilities to think or at least to consider science cool and interesting. She is currently in the 4th Grade with 5th coming after the Summer.
She reads basically at her own grade level so while I'm open to stuffing the Kindle with books to be read when she's ready, I'd like to focus on giving her books she can read now. Ender's Game will be on there most likely. Game of Thrones will not.
What books would you give a youngling? Her interests currently trend toward the young mystery section, Hardy Boys and the like, but in my experience she is very open to trying new books with particular interest in YA fantasy but not much interest in Sci Fi (if I'm doing any other optimizing this year, I'll try to change her opinion on Sci Fi).