In response to your concrete question, if you want to say text me - send me a notice - drop me a message or something alike, you can say:
- schick / schreib mir eine Nachricht
- schick / schreib mir eine SMS/WhatsApp/etc... (more specific)
But there are the expressions inform me - notify me - let me know as well. Then you could say:
- gib mir Nachricht (benachrichtigen - http://www.duden.de/suchen/dudenonline/Nachricht%20geben . Not used though)
- gib / sag mir Bescheid
It's not totally clear what the exact context is in your question, but I hope it helps.