Yes, if you qualify for both, but they can't be on the same person.
To qualify for EITC with a dependent, it must be a "qualifying child dependent", which is to say, your own child or a close relative, under the age of 19 (or a full time student under age 24), who lives with you half the year.
A qualifying child dependent also qualifies for the $2000 child tax credit until age 16, and then the $500 other dependent credit after that. So your child between the age of 17 and 24 might get the "other dependent" credit of $500 but still make you eligible for EITC.
Or, you might have one child that makes you eligible for EITC, and a different person who qualifies for the other dependent credit, such as a non-related person who lives with you all year, or a parent you support.
Or, if your dependent is not a qualifying dependent, but you are between the ages of 25 and 64 with low income, you might qualify for the version of EITC that does not require dependents (a lower payment) and then get the dependent credit for the other person.
