When an employee receives a paycheck in the United States, one of the deductions from the check is social security. I once tried to get this removed from my paycheck and the payroll company told me that they can not do this. Due to this, I was wondering if there is some sort of law that requires employees to pay Social Security?
There sure is: the Federal Insurance Contributions Act (FICA). See 26 USC 3101.
In addition to other taxes, there is hereby imposed on the income of every individual a tax equal to 6.2 percent of the wages (as defined in section 3121(a)) received by the individual with respect to employment (as defined in section 3121(b)).
Moreover, your employer is required to withhold this tax from your wages. See Section 3102.