Am I entitled to a stimulus check if I use an itin but my daughter is a citizen ?

No.  You cannot claim the child tax credit unless the child has a valid SSN and the stimulus for a dependent under age 17 is based on qualifying for the child tax credit.

Why does a US citizen not have a SSN?

You are not entitled to a stimulus payment, for either yourself or your dependent, if you do not have a Social Security number that is valid for work. Your daughter's status doesn't make any difference.