Short answer. Yes. Article 1870 of the Civil Code recognizes that acceptance by an agent may be implied from his acts which carry out the agency. By performing the assigned tasks, you have accepted the agency through your conduct — no verbal or written acceptance is required.
What the law says
Acceptance by the agent may also be express, or implied from his acts which carry out the agency, or from his silence or inaction according to the circumstances.
Civil Code, Article 1870 — Acceptance by the Agent. Read the full provision →
Conduct as the clearest form of acceptance
Article 1870 sets out three ways an agent can accept: by express words or writing, by acts that carry out the agency, or by silence and inaction depending on the circumstances. Performance is the most straightforward of the three. When you begin executing the very tasks the principal assigned you, the law reads that as consent. There is no ambiguity in conduct: you received the appointment and then did the work. That sequence answers the question of acceptance without requiring any spoken or written confirmation.
What being bound to the agency means for you
Acceptance binds you to the full set of obligations that come with the role. You must act within the scope of the authority given, exercise the diligence of a good father of a family in managing the principal's affairs, account for money or property you receive on his behalf, and refrain from exceeding your authority without prior approval. You cannot claim the benefit of acting as agent — for example, relying on the principal to indemnify you for expenses — while also disclaiming the corresponding duties. The relationship is accepted whole.
Partial performance and mixed signals
If you performed only some of the assigned tasks, the implied acceptance may be limited to those tasks. However, the practical difficulty is that once you have acted on any part of the agency, your principal reasonably expects you to continue. Stopping partway without notice, and without giving the principal a reasonable opportunity to arrange alternatives, exposes you to a claim for damages. It is safer to complete what you started — or to give clear, timely notice that you are declining the rest — than to leave the principal uncertain about your status.
If you want to end the agency
Having accepted through conduct, you cannot simply walk away without consequence. The proper route is to give due notice of your withdrawal to your principal. Importantly, even after giving notice, you must continue to act until your principal has had a reasonable opportunity to take the necessary steps to address the situation. An abrupt withdrawal that leaves the principal exposed to harm may result in a damages claim against you. The scope of your obligation to continue will depend on the circumstances and how time-sensitive the principal's affairs are at the moment of withdrawal.