rock-climbing n.

by 1887, originally "the more showy branch of mountaineering" according to the author below:

Even though rock climbing be inferior as an art to snowcraft, it must still be practised properly. Let not the seductive charms of rock climbing occupy too large a place in the mind of the young mountaineer to the exclusion of snowcraft, lest he be but preparing for himself in matters athletic a sad old age. [C.T. Dent, "Mountaineering," London, 1892]

The modern sport of rock-climbing emerged c. 1993. Rock-climb (n.) "an ascent of a rock-face," is by 1895. Rock-climb as a verb is by 1934.