That is one reason the bank would be asking for your Social Security number. Another would be that your father has asked that you be added to the CDs as a "pay on death" beneficiary. It would be reasonable for you to ask him for what reason the bank needs the number.
If he is adding you as a joint owner, you might be able to borrow against the accounts, but you will have to ask at the bank. The bank may have a requirement that all owners of the CDs agree to their use as collateral.
If he is adding you as a beneficiary, you don't get any ownership rights until he dies. Borrowing against the CDs would not be possible in that case, unless your father pledged them as collateral for your loan.
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That is one reason the bank would be asking for your Social Security number. Another would be that your father has asked that you be added to the CDs as a "pay on death" 