Actual rods can be bought in stores, though only fishing shops in Vermillion City and near Lake Rage sell Super Rods. In VR, however, the quality of the rod doesn't determine what pokemon someone can catch, but rather how long-lasting the rod is. An old rod, for example, is only good for a few catches before it breaks.

It is possible for a character to put together something akin to a rod with random trash items, but this sort of rod wouldn't have much lasting power. You might be able to get one or two catches out of it, if that, before it breaks. Catching Pokemon just takes a lot out of a rod.