I want to study again after working for 1 year in the US. Do I have to apply for student visa in my home country ?

I am an Indian. I graduated from a college in US in May 2014. Thereafter I worked on OPT for a year. My H-1B Visa did not come through, and my OPT expires in July 2015. I want to do my Master’s in Finance in the US. The course begins in September 2015. So, do I have to go back to India to get my student Visa or can I apply here in the US ?

If you get an admission before your OPT expires and your I20 is issued before your 60 days grace period is over, you may continue to stay in US. The key is that your new school should issue the I-20 before your 60 day grace period after OPT expiry. Speak to the DSO at the new school that you plan to apply so that they can help you. You may read the Washington University OPT Grace Period Section

if your new school issues i20 before your grace period. then you can directly transfer from old school to new school.