No, not if it's "earned income" (meaning wages, either on a W-2 or 1099-MISC). He'll need to file his own return for that. And if he's not required to file, he may want to file anyway in order to recover taxes withheld.
Under certain circumstances, IRS allows a parent to include "unearned income" (generally, investment income) on the parent's return. If that situation applies, see this link to IRS Tax Topic 553 discussing the criteria: https://www.irs.gov/taxtopics/tc553.html