Turbo says I cannot claim myself as a dependent . Can I claim myself as an exemption ?

There is no exemption. 

Federal personal exemptions were eliminated some years ago. You now get a higher Standard deduction.

Are you asking about some State tax provision?

Just by filing a return you are claiming yourself.  Unless you check the box that says you can be claimed by someone else.  All you have to do is enter your name and ssn under My Info.