The bill was approved by a vote of 108-9. It builds on a 2006 law making it illegal for young drivers to use a cell phone, applies to all drivers.
Violators could face a $100 fine plus court costs.
A final House vote could come Thursday. A similar plan previously failed in the senate.
Ten states and the District of Columbia currently have a text messaging ban for all drivers, according to the national Governors Highway Safety Association, which represents state highway safety agencies. Two months ago, the association listed only seven states with the ban.
Several groups, including the AAA Carolinas motor club and AT&T North Carolina, support the texting ban.