There isn't a proper translation. The translation changes depending on the context in which it is used. Keep in mind that it is a negation, also used to form rhetorical questions or a reinforcement (I prefer to call it a "modulator") of denial. To translate that, in terms of meaning, you can use many adverbs or sentence structures. As far as I know, there are no words in English that also have the informal connotation of "mica" and its "rhetorical value".
Let's start with easy examples of how to modulate the negation:
Non glielo dico mica! | (Surely) I'm not going to tell him about that!
Non capisco mica la tua domanda. | I don't understand at all your question.
Mica male! | Not bad! (In this case maybe you could use "Quite good!", or I found this translation "It’s not hardly that bad." too.)
Mica male questa domanda. | Not bad, this question.
"Mica" can be used in the context of fear that something that we don't want is happening, hoping for a negative answer but fearing for an affirmative one. Read these examples (the translation is quite hard so don't consider the translations as good ones):
Non mi denuncerà mica per questo? | He won't sue me for that, will he?
Non si sarà mica fatto male! | He wouldn't hurt himself, has he?
Non sarà mica partito senza il casco! | I hope that he has not left without his helmet!
Now the next are more difficult to understand because there is the rhetorical meaning.
This first one supposes that we take into account the possibility of a negative answer:
Hai mica una sigaretta? | By any chance would you have a cigarette?
The sense you should try to convey is that the person who is using "mica" knows that the person he/she is talking with thought a determinate thing that isn't true.
Non voglio mica fregarti! | (I know that you think but) I really don't want to rip you off!
For me, even this one has this sense:
Non gli credo mica! | I don't believe him at all!
Google translate in the past could not translate mica because it is common only in spoken Italian while Google mainly used books and written material to translate texts!
;-)Unfortunately it's not possible and mica, as well as other common adverbs (più, meno) or even pronouns (ne), is a word that has no exact correspondent in English. Also the converse is true: thereof comes to mind immediately.