Sure. It's a verb. "I am trying".

Can you give me an example? Do you mean something like "I am trying to get this car to start" where it is a something you are doing at that moment in the present? The answer is yes. The verb try can be used in continuous time. You could use it in the future too, "Tonight at 5:00, he will be trying to be the only pitcher in history to pitch two consecutive perfect games." and past continuous "I was trying to get it to work last night, before I went to bed..."

Try is a transitive verb and surely can be used with the continuous tense too.