A new and distinct variety of climbing rose plant herein referred to by its cultivar name, ‘Radwire’, is provided which forms in abundance on a substantially continuous basis attractive, cup-shaped, deep pink blossoms. The vegetation is vigorous and the growth habit is very bushy and climbing. Attractive, semi-glossy, medium green foliage is formed. Excellent disease resistance is exhibited, particularly for black spot, rust, and mildews. The new variety is particularly well suited for growing as distinctive ornamentation in the landscape.