If all you earn is social security then no. If you have other income aside from the social security then it is taxed based on a graduated scale of what you earn in total. You can go to IRS.gov and find the information you need there for your situation.
Your S.S. Is only taxed if it's over a certain amount each year. The best thing to do would be to contact Social Security and ask them. You can also contact the IRS and find out.