I am writing a resume for a doctoral application. In my current job, I am an Assistant Professor (tenured). However, besides being young, I don't have a doctorate or postdoctoral degree. I am also not a genius or a prodigy. In my country, the way you manage to be a university professor is different from other countries. If you want to work at a federal public university, for example, you take a test with several stages, and in some cases, people with only a master's degree and young people can get the job. I am still starting my career as a professor and researcher; I have no papers published in high impact journals. I don't want to look like something I'm not, but it also shows that I have some merit in having this position. I would like to know my title in an international context, specifically in the USA. My first option was a Full-time Lecturer (permanent appointment).
List your job title as specified in your employment contract. Anything else is a lie. You can translate it into English or give it in both languages.
Since this situation may be unfamiliar to doctoral programs in the USA, give a brief description of your duties for the job, such as "Teaching introductory environmental science."
There is nothing wrong with seeking a PhD when you are already an assistant professor. I get emails from people in your situation from time to time seeking positions. The problem these people have with their applications is that they do not explain why they want a new position. If you can give a good reason, your current title will be an advantage.
Job titles have no international context. They have only a local context. (They don't even have a national context. American academics can all easily figure out that Professors at SUNY Adirondack, SUNY Geneseo, and SUNY Stony Brook - all universities in the same state system - are vastly different jobs with vastly different qualifications.)
Just give your official title (in the local language if not English - this emphasizes that it's not translatable).
In the rest of your application materials, you can explain what your job duties are and what qualifications you have, and people will figure it out.