Currently no.
http://www.happyschools.com/options-h4-visa-spouse-2/
If your hu*****and is in H1-B status, currently DHS is proposing letting spouse of H1B to work. The rule has not finalized, and even if the rule is passed, you'll need to apply for an EAD. So you won't be able to work until that happens.
http://www.happyschools.com/ead-for-h4-visa-holders-spouses/