You can include anything you want in your CV as long as you use precise language. Your “abandoned patent” sounds like it’s not actually an abandoned patent but is an abandoned patent application. Personally I don’t think it will be of much, or possibly any, value on your CV, but whether that’s the case or not would depend on the specific nature of the invention you tried to patent and the reason for abandoning the application. I can imagine hypothetical (though unlikely) scenarios where it might be worth mentioning. And even if you don’t mention it on your CV, the story of the abandoned application can still make for a nice anecdote to mention in an interview or a statement of purpose.
Regardless, whatever you do, do not use the word “patent” to refer to something that has not been approved as an official patent by the US Patent and Trademark Office or some other national or international patent registration agency. The correct phrase to use in your situation is “patent application”. A related term that people sometimes use for applications that are under review by the patent office is patent pending, but that only applies to applications that are still pending, and yours isn’t since it’s been abandoned, so you shouldn’t use that term either.