You probably want to file this under “Solution in Search of a Problem” — Nokia has patented the bright idea for alert ink. The idea is to use ferromagnetic ink to create a tattoo that “pairs with your phone” and vibrates when you get an alert. For those not into body art, there’s also the option of a badge.

Although if you do get a tattoo for this, Spider-Man would be a fitting one.
Yes, almost everyone constantly has a phone on them at all times now and you might not feel your phone vibrate, but getting your body modified seems like a heck of an adjustment for minor gain. Plus, as someone who already suffers from phantom vibrating, this would absolutely drive me nuts.
Also, if you have a heart condition, consider not getting this on your left arm.

"Either I just got a text or I need to get to the doctor."
Depends where you get the Tat.
Ooooh!!! Text me again!!!! yeah baby, like that!