It is, but we don't call our bodies 'our organisms'. We also don't generally call them a lot of other things that they are, such as "our collections of tissues and cells".
If someone said, "How much alien DNA do you have in your organism?", I'd think "What organism? I didn't know I had an organism. I've got a car and a dog but I'm pretty sure I don't own an organism!"
If you have a question about the English language and would like to ask one of our many English teachers and language experts, please click the button below to let us know: