Yes, an agent can you find an apartment; whether or not they charge depends on the situation.
I know agents who regularly help people find rentals and are paid by the listing brokerage if they successfuly bring them a tenant. If the tenant finds something on his or her own, then the agent does not get paid; that happens, but is just part of being a real estate agent.
I know agents who charge a retainer fee of a couple hundred dollars which is credited against any commission earned. Rentals can take a lot of time and even if successful, result in a very small commission.
Agents can show you rentals listed in the local MLS, which typically offer a commission, or they can help you find a rental by owner, however, in those cases, the tenant client would be responsible for compensating the agent, because owners typically do not offer a commission to agents.