climber (n.)

early 15c., "one who climbs," agent noun from climb (v.). Botanical meaning "a plant that rises by attaching itself to some support" is from 1630s.

Climbing plants are distinguished as stem-climbers, which like the hop, wind upward around an upright support, and as tendril-climbers, which, like the grape-vine, cling to adjacent objects by slender coiling tendrils. Other plants climb also by means of retrorse bristles or spines, or by means of rootlets. [Century Dictionary]