Aparently, YES! it's called "plant patents" acording to:https://plantlaw.com/2018/10/30/copyrig ... t-variety/
"PLANT PATENTS ARE SURPRISINGLY SIMILAR TO COPYRIGHTS
You’re a plant breeder. You have a great cultivar that you want to propagate and sell. You would really like to put it out there so that all your hard work could pay off and so that everyone could enjoy how great your cultivar is. Of course, you don’t want to sell one plant and then have the buyer of that one plant become your competition by using it to make and sell numerous clones. You want to be the only one who can sell clones, or you want people who sell clones to have to do so with a license and pay you royalties. Seems fair, right?
.......... (the dots are added in by uxleumas)
Something that most people (even most patent attorneys) do not know is that plant patents are very much like copyrights for plant cultivars. Plant patents only cover exact genetic copies (asexual clones) of the patented cultivar. They do not protect sexual progeny (plants grown from seeds) or plants that are merely similar to the patented cultivar. So, in that way, a plant patent is essentially a copyright on a plant cultivar.
In contrast, a “plant patent” protects a unique, original genetic combination that started as a single plant. The plant patent also covers all individual plants with the same genetics — asexual copies of that original plant.
So, to review:
A utility patent relates to an inventive idea and can cover anything with certain similarities to that idea, depending upon how it is claimed.
A copyright protects against actual copying of an original work.
A plant patent protects against actual copying of an original genetic combination.
Hmmmm… maybe you CAN (almost) copyright a plant. Get a plant patent.
FYI, plant patents are much less complicated, much less expensive, and issue much more quickly than typical utility patents. So, if you’re a plant breeder, do not be intimidated by the term “patent.” Think of it as something like a copyright.*
*Because I’m a lawyer, I have to point out that a plant patent lasts for 20 years from the filing date, while the term of a copyright is much longer; and that copyrights exist automatically upon creation of an original work, while plant patents must be applied for and granted before the rights exist. So there are some important differences. ........."
so, you indead can "copyright" your own plant, but you have to fill out a few papers and stuff. good luck!