My girlfriend told me that she was pregnant and had a sonogram on aug. 9. The sonogram had concluded that she was 7 weeks and 4 days in. We had been split up for most of June and all of July but she says that she was with no one else in that time. The last time that we had sexual intercourse was on June 7. Is it possible that I am the father?

Yes its possible you're the father. The timing of the last time you slept with her and amount of weeks she is pregnant do add up give or take a few days.
Sperm can live in the vagina for up to 5 days and the amount of weeks pregnant the doctor tells you is never 100% accurate, only 5% of women actually give birth on their due date. The only way you can be completely sure is to have a DNA test when the baby is born.