RALEIGH, N.C.—Venomous snakebites are on the rise in the Sunbelt this summer, with North Carolina, Georgia and Texas on track to set records.

In North Carolina and Georgia, venomous snakebites have been rising for the past several years and are up more than 10% from a year ago, according to the states’ poison-control centers. In Texas, there were 415 reported snakebites in May and June, 27% more than the same period five years ago.

Copperheads...