It's certainly possible to get on the road to your CFA qualification whilst you're still at Uni. It's actually becoming more and more common for final year students to study for, and take, their Level I exam before they graduate. However, your selected exam date must be within 11 months of your graduation month for your bachelor’s degree or equivalent program.
Once you've graduated, you can then register for your Level II Exam, and go from there.
There's a lot more information about the requirements on the CFA's website here:
Become a CFA charterholder through CFA Institute. Learn about the eligibility requirements to obtain your CFA designation.
In summary, you'll need to pass all three levels of the CFA program exams, complete 4 years of relevant work experience ('relevant' means being somehow involved in the investment decision making process) and then submit professional references to be awarded your charter.
It's a lengthy process and a big-time commitment - candidates typically budget 300+ hours of study for each level - so getting your Level I exam done in conjunction with your final year of studies can be a big help. Especially if there's a big overlap in what you're studying at Uni.
Have a look at that CFA website link and let me know if you have any other questions.