I joined a company for CPT with an hourly pay of 20$ in California two weeks before.
I am in F1 student visa. How much percentage will the Federal and State tax would be?I still haven't received my first pay yet.
Do I have to pay social security and medicare taxes?

On F1 and OPT you are exempt from residency for 5-years. That is you must file non-resident tax return. Your wages are exempt from social security and Medicare taxes. If employer withholds, these taxes then tell them that they should not withhold FICA taxes. For non-resident filing, read:
Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents (http://taxipay.blogspot.com/2008/03/us-tax-filing-requirements-for-non.html)