Social Security disability insurance is called "insurance" for a reason. You pay a premium from every paycheck, and receive disability coverage in return. How much is the premium? See this table.
15.3% of your wages are withheld for Social Security. Your employer pays 7.65% and you pay 7.65%. If you are self-employed, you pay the entire 15.3% yourself. Of this amount, 10.6% is for Social Security "retirement," 2.9% is for Medicare, and 1.8% is for disability insurance.