The usage is correct, but it's unclear which part you are calling into question.

At the top-level we are using the word "can" in a typical fashion: "I am eating cake" -> "I can eat cake" is analogous to "I am having it mailed to you" -> "I can have it mailed to you."

Within the sentence "I am having it mailed to you" there is a structure whose name I don't know. Compare with "I am letting him speak to you" and "I am watching you speak to her."