We introduce a new kind of singular beam with a controllable topological charge. These beams are created by modulating the spatial phase using a tangent function on the angular coordinate, and a linear function on the radial coordinate. While the angular function controls the topological charge of the beam, the radial function generates a warped intensity profile. We simulate several cases to analyze their evolution with propagation and determine their topological charge. The results are supported with an experiment using a Shack–Hartmann wavefront sensor.