Short answer. Yes. Article 721 of the Civil Code provides that by intellectual creation, the author acquires ownership with regard to his literary, dramatic, historical, legal, philosophical, scientific, or other work. As the author of your book, article, or play, you acquire ownership of it by the act of creating it.
What the law says
By intellectual creation, the following persons acquire ownership
Civil Code, Article 721 — Ownership By Intellectual Creation. Read the full provision →
What the law says
The author with regard to his literary, dramatic, historical, legal, philosophical, scientific or other work
Civil Code, Article 721 — Ownership By Intellectual Creation. Read the full provision →
What the law says
The painter, sculptor, or other artist, with respect to the product of his art
Civil Code, Article 721 — Ownership By Intellectual Creation. Read the full provision →
Ownership by intellectual creation covers your kind of work
Article 721 answers this directly, and a book, article, or play falls squarely within the category it names: the author with regard to his literary, dramatic, historical, legal, philosophical, scientific or other work. A book or article is literary work, and a play is dramatic work, both named specifically in the article, so ownership by intellectual creation applies to what you wrote.
Ownership arises from the act of creating it
The article frames this as a mode of acquiring ownership in itself: by intellectual creation, the following persons acquire ownership. The acquisition is tied to the creative act, not to registration or any further formal step described in this article. Writing the work is what the article treats as the event that gives you ownership over it as its author, before anyone else does anything with it.
The article recognizes several kinds of creators, not just authors
Article 721 is not limited to written work. It also covers, for example, the painter, sculptor, or other artist, with respect to the product of his art. Composers, scientists, and technologists are named as well. Seeing your case, as an author of literary or dramatic work, alongside these other categories shows that the article treats intellectual creation broadly as a source of ownership, with the author's own written work as one clear application of the same principle.
What this means for what you wrote
As the author of your book, article, or play, Article 721 places you within the class of persons who acquire ownership by intellectual creation. You do not need a separate act beyond having created the work for this article to apply to you as its author, and the article does not condition that ownership on the work having been published, registered, or shown to anyone else first.
What this article does not address
Article 721 establishes that ownership arises from the act of creation itself; it does not itself walk through how that ownership is exercised afterward, such as licensing the work to a publisher, transferring rights to someone else, or what happens if two people claim to have created similar work independently. Those are separate questions governed by other rules. What this article settles is the starting point: as the person who wrote the book, article, or play, you are the one who acquired ownership of it in the first place, before any of those later questions arise.