Yes, you can. We protect and copyright logos as creative expressions of an idea. As long as you have created original work, you can copyright protect it. This does not apply to logos used for business purposes.
As such, a logo can be protected by both copyright and trademark, depending on how it is used..
A logo copyright protects a creative intellectual design or an expression of an idea, while a logo trademark protects things that identify a business on the marketplace.
This means that you can copyright protect your logo design the moment you create it.
Copyright your logo