An anchoring system and method for anchoring a climbing head to a concrete slab. The anchoring system includes a support and adjustment means for adjusting the positioning of the support with respect to anchoring means of the support. The adjustment means includes a first element fixed to the support, a second element fixed to the anchoring means, both the first element and second element being coupled to one another through a plurality of respective teeth forming a laterally detachable attachment which allows varying the relative longitudinal position of the first element with respect to the second element through the engagement of the corresponding teeth (32, 36) regulating the positioning of the support with respect to the anchoring means.