Assuming that the content written is itself not a derivative work (e.g., not fan fiction), and that the author has copyright over the work (which is the default situation):
Copyright attaches when the work is set forth in a "tangible medium", which is "when its embodiment in a copy or phonorecord, by or under the authority of the author, is sufficiently permanent or stable to permit it to be perceived, reproduced, or otherwise communicated for a period of more than transitory duration."
Skipping past the legalese, basically, when it was typed on a computer or written on paper, the author obtained copyright over the work. Part of copyright is the ability to control derivative works, such as a reading. So if the author has copyright, the author can read it aloud and post the recording on YouTube, creating a derivative work of their material.
- If the material is a derivative work, and not fair use, a) the original material is under the control of the original copyright holder and b) the audio version of the material is as well.
- If the author was paid to create the original work, as a general rule subject to their contract, the one who paid to create the work owns the copyright, and their approval is necessary to make the derivative audio recording.