Yes, there is an age limit on claiming your child as a dependent, but it depends on whether the child meets the criteria for a "qualifying child" or a "qualifying relative."
To summarize, for a child to be claimed as a dependent under the "qualifying child" criteria, they must be under 19 years old, or under 24 years old if they are a student, unless they are permanently and totally disabled. For a "qualifying relative," there is no age limit, but the child must not meet the criteria of a qualifying child for you or any other taxpayer.
Sources:
Notice 2018-70
§ 152. Dependent defined
Publication 1380
CCA 200812024
Publication 501 (2023)