It's absolutely possible to transfer from a community college to an Ivy League school if you're a dedicated student. In fact, transfer students often have an edge over high school students. You've already shown that you can succeed in a college environment, so you're much less of a risky admit for these schools. You'll also be competing against a smaller pool of applicants where it's easier to get noticed. I just read this quote in an article on community college students transferring to four year colleges:
Increasingly, highly selective colleges including some of the Ivies are welcoming outstanding community college transfers, who tend to perform well and participate in the life of the university, said Rod Risley, executive director of Phi Theta Kappa, based in Jackson, Miss.
Phi Theta Kappa is the main honors society for community college students, so this brings up another important point. If you want the best chance at being accepted as a transfer applicant, you should make sure you have awesome grades in (at least a 3.5 GPA) first and foremost. You should also make sure you're taking the appropriate classes to affect a smooth transition from community college to a four year college. Do some research to see whether your credits will transfer appropriately. I'd also recommend that you participate in activities that demonstrate leadership skills and a passion for your intended major. These could be internships, clubs, scientific research, or any number of other things that are related to your interests.
If you had circumstances in high school that led you to perform poorly, don't be afraid to mention this in your essay. Colleges love to see people who have been able to recover from tough situations and rededicate themselves to pursuing ambitious goals.
Keep in mind that some Ivies accept more community college transfers than others. The most competitive Ivies accept very few CC transfer students. Harvard accepts less than 5 a year, and Yale is nearly that low. Princeton doesn't accept any transfers.
However, some of the other Ivies do offer programs that are much more friendly to community college students. Cornell accepted 157 transfer students from two year colleges in 2013, although this is a slightly deceptive statistic. Only the College of Arts and Sciences is technically considered a part of the Ivy League even though Cornell has many other colleges under its umbrella.
Columbia also accepts quite a few community college students into its School of General Studies, which "serves nontraditional students who have had a least a one-year break from high school." UPENN only admitted 15 transfer students from community colleges to its regular undergraduate program between 2009 and 2013, but it also has a special liberal and professional studies program that is very similar to the School of General studies. This program admitted almost 150 CC students in that same four year period.
I'd recommend that you check the information pages on this site to learn more about the deadlines, requirements, and likelihood of acceptance for all the Ivies.