If my child was a full time college student not living at home but I paid for living expenses, can I still claim him as a dependent?

Living expenses are not deductible. But if your child was away at school, that is a temporary absence that allows you to say he lived with you.  Does he fit the other criteria to be a qualifying child?  (Under 24, full-time student...)

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent

It depends on what you mean by "not living at home".  If he is only not living at home for purposes of attending school, even if living off campus, that is only a temporary absence. He is still considered as living with you for the Qualifying child rules.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year   (not even one night at the non-custodial parent’s home).
2. His/her gross taxable income for the year must be less than $4200 
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer