Am I able to use my social security card or birth certificate as proof of identity if I lost my identification card?

That depends----where or who are you trying to prove your identity to?

I am trying to get an advance on my tax return with TurboTax and it is on my document checklist to provide my ID card to prove my identity. But I misplaced my ID. 

@tolpagirl No---you will not be able to get the refund advance using a birth certificate or SS card.  Sorry.