Strictly, no, there is no way. There is an imperfect way but it wouldn’t be used often; it is not a direct manner of asking oneself. It is imperfect because the question is put to anybody, although as well to oneself.

• Je demande à savoir pourquoi je ne peux pas pleurer.

• In my journal I wrote about my emotional blockages, by writing out questions to myself. In one question, I asked myself, "what is the reason that I can’t cry?"

• Dans mon journal j’ai écrit à propos de mes blocages émotionnels sous la forme de questions que je pose à moi-même. Dans l’une des questions, je demande à savoir pourquoi je ne peux pas pleurer.

The meaning doesn’t changes that much with a pronominal use, when you wonder something, you are kind of asking yourself a question a figurative way.

A verb that can be used to avoid a pronominal construct is chercher:

Je cherche pourquoi je ne peux pas pleurer.