No, having a vasectomy doesn't increase your risk of getting prostate cancer. Many studies have been performed to see if there is a link. The best current evidence indicates no increased risk of prostate cancer after vasectomy.
If you're concerned about your prostate cancer risk, talk to your doctor about possible symptoms and screening tests. You're at increased risk of prostate cancer if you're older than age 50 or if you have a close family member with prostate cancer.