"Komm' schon" would probably be the more fitting translation for "come on" for encouragement or prodding. "Komm' jetzt" is more like "Come now". An impatient mother might say that to her dawdling child.
"Komm' jetzt" on its own is quite harsh, like an order or a command. You might want to think about whether you get to order the recipient around or not ;)
As a part of a longer sentence, "komm' jetzt" is less harsh, but still somewhat pushy. You might find it in advertisements, for example:
Komm' jetzt zu Superkauf und spare!
Hurry to Superkauf now and save (a lot of money)!
Kommt jetzt alle zur Kirmes!
Hurry now to the carnival, everybody!
Just in case somebody wonders what the apostrophe in komm' means: It signifies that komm' is a shortened version of komme.