No. Under the General Data Protection Regulation, a data subject is an identified or identifiable natural person. An AI agent is software, so it cannot be a data subject in its own right.
However, the GDPR may apply when an agent processes personal data relating to an individual. This could include account information, identifiers or activity linked to the person using the agent.
In such cases, the individual is the data subject, not the AI agent. Organisations must therefore consider whose personal data the agent processes and how that data is collected, used and protected.