This hinges on whether the monster has sufficient capacity to be responsible for its own actions. An animal, a child, or an insane person does not have the reasoning capacity (under the law, I'm not looking to get into a scientific discussion) to weigh consequences and make choices accordingly, and therefore be held responsible for their poor choices. Frankenstein certainly INTENDED for the monster to be more reasonable than an animal, a child, or an insane person, and the monster's monologues would seem to indicate that he succeeded. I'm trying to recall one of his final monologues, where he (the monster) seemed to display a knowledge of right and wrong; if this was the case, this would mean he 100% had the ability to tell right from wrong, but just chose not to, and ergo, he is responsible for his own actions. This is the crux of the case.

Questions about "should Frankenstein have ever created him in the first place" are a giant strawman, since no criminal, or saint, ever asked to be born they way they were, either.