can I claim my fiancé's daughter

It depends. If her mom works and can claim her as a dependent on her return, even if she chooses not to, then you would not be able to claim her as the first criteria for a non-relative to claim someone is that they cannot be a qualifying child of any other tax payer.  

 If her mom is not filing a tax return, then if she meets the criteria to be a Qualifying Relative, then you may be able to claim her for the $500 Other Dependent Credit and file as Head of Household.  You can NOT claim her as a qualifying child or for the child tax credit or Earned Income Tax Credit, so it is possible that when you remove those credits, you may not find a benefit to claiming her as a dependent. 

Qualifying Person for the ODC
A person qualifies you for the ODC if the person meets all of the following conditions.
1. The person is claimed as a dependent on your return. See Pub. 501 for more information about claiming someone as a dependent.
2. The person cannot be used by you to claim the CTC or ACTC. See Child Tax Credit (CTC) , earlier
3. The person was a U.S. citizen, U.S. national, or U.S. resident alien. For more information, see Pub. 519. If the person is your adopted child, see Adopted child , earlier.

https://www.irs.gov/publications/p972