My daughter is a full-time college student, can I claim her as my dependent. When she file her return can she claim herself as a dependent?

If you claim your daughter as a dependent on your income tax return, she cannot claim herself on her income tax return. If your daughter is filing her own tax return, then she can be claimed as a dependent on your return, but she cannot claim her own personal exemption. In this case, your daughter should check the box on her return indicating that someone else can claim her as a dependent.