My answer for your question is "I'll give it a try".
In your sentence, "か" doesn’t come at the end with "?" mark, so that sounds like "自問自答" for me. I'm not sure about how to translate this kind of Japanese four character idiom but I should say "asking oneself a question". For example, I ask myself for something that (“頑張るしかないか？”, then say "Yes") = 頑張るしかないか. This means I don’t know if I can do it, but no choice I'll give it a try.
Hope this will help.