Yes, but a person born in 1890 would have been 45 in 1935 and would have been issued a card. I can state this with absolute authority as my grandmother (b. 1900) had a social security card issued in 1935, it came into my possession after her death.
The article doesn't state that the card was ISSUED in 1890, it states that the cardholder was BORN in 1890.
So my point still stands, for Obama to be using this number he would 1) have to be over 100 years old, or 2) its fraudulent.