Short answer. It is yours. Article 503 classifies rain waters falling on privately owned land as being of private ownership, as long as they remain within the boundaries of that land. Once the rainwater leaves your property's boundaries, this particular private-ownership classification no longer applies to it.
What the law says
The following are of private ownership: (1) Continuous or intermittent waters rising on lands of private ownership, while running through the same; (2) Lakes and lagoons, and their beds, formed by Nature on such lands; (3) Subterranean waters found on the same; (4) Rain waters falling on said lands, as long as they remain within the boundaries
Civil Code, Article 503 — Waters Of Private Ownership. Read the full provision →
Rainwater on your land is expressly listed as privately owned
Article 503 lists several categories of water found on privately owned land as being of private ownership, and item four covers exactly your question: rain waters falling on said lands, as long as they remain within the boundaries. So rainwater that falls on your private property belongs to you under this article, in the same way the article treats other waters closely tied to privately owned land, such as waters rising on the land while running through it, natural lakes and lagoons formed on it, and subterranean waters found beneath it.
The condition that keeps the water yours
The private ownership over rainwater is expressly tied to the water staying within the boundaries of your land. This is not an unconditional, permanent claim over every drop that ever touched your property; it is a classification that applies specifically while the rainwater remains on your land. Once rainwater flows off your property, whether into a public watercourse, a neighbor's land, or elsewhere outside your boundaries, this particular basis for private ownership no longer covers it in the same way.
Why the law ties ownership of rainwater to the land itself
This provision reflects a broader pattern in Article 503, where several kinds of water closely connected to a specific piece of private land are treated as belonging to the landowner precisely because of that connection, rather than being treated as part of a larger public water system by default. Rainwater falling directly onto private property is the clearest example of water whose presence is entirely tied to that specific land, which is why the law recognizes it as private property for as long as it stays there.
What this means for how you use it
You are entitled to collect, store, and use rainwater that falls on your land and stays within its boundaries, since Article 503 recognizes it as your private property rather than something belonging to the State. If you channel that water off your property, for instance through drainage into a public waterway, it is worth being mindful that the water's status can change once it leaves your land, since the private ownership described here is specifically tied to the water remaining within your boundaries.