Formal:
* Estou tentando aprender português. (This is the most literal and formal translation)
* Estou a tentar aprender português. (This is another formal option, especially in European Portuguese)
* Estou a estudar português. (This is a more formal and specific way of saying "I am studying Portuguese")
Informal:
* Estou aprendendo português. (This is a more natural and informal way to say it)
* Estou a aprender português. (This is another informal option, especially in European Portuguese)
* Estou a dar os meus primeiros passos em português. (This means "I am taking my first steps in Portuguese" and is a good way to express that you're a beginner)
The best choice for you will depend on the context and your relationship with the person you're talking to.