Question: Is there a chance that I can transfer into a college that already denied me?
Yes, it's definitely possible to be admitted as a transfer student to a college that already said "No" to you. However, here are some things to keep in mind:
1) You will probably need a full year of college grades to show to your prospective transfer school, so if you try to transfer as a freshman--depending on the application deadline--you may only have one semester of college grades to submit. So you're probably better off aiming to transfer as a junior (or perhaps halfway through your sophomore year).
2) Colleges do routinely admit students who have been successful at other colleges even if they were not admissible back in high school. However, you need to make sure that, if you were already turned away, your college record is stronger than your high school record was and that you have something else on your application that will make you an attractive candidate, too (e.g,. strong extracurricular or community involvement at your college, research or internship experience, a paying job).
3) Ivies and a handful of other hyper-selective schools (Stanford, MIT, etc.) are in a class by themselves. They turn away many highly qualified freshman applicants for no apparent reason, so it can be tough to "do better" and then reapply. They also take very few transfers. Typically, Ivies and their ilk don't admit students they already turned down. Sure, there are exceptions, but it isn't common unless the applicant can point to some big-time achievements since the denial.
So, if you have your sights set on a school that already refused you, it may be possible that you'll get another chance. Meanwhile, try to recognize the pluses of your current situation and be sure that, if you do decide to transfer, it's really for the right reasons and not just to prove to anyone--including yourself---that the folks who said, "No thanks" really made a huge mistake.