The aim of this paper is to construct representations of the quantum group \(SU_ q(2)\) for \(q\in(0,1)\) using an analog of the orbit method (geometric quantization). First the author studies the relations between functions on \(SU_ q(2)\), the deformed universal enveloping algebra of \({\mathfrak {sl}}(2,\mathbb{C})\) and functions on \(AN_ q\), where \(AN\) denotes the solvable part in the Iwasawa decomposition of \(SL(2,\mathbb{C})\). Next he discusses quantum dressing orbits, which turn out to be quantum two- spheres and constructs the quantum analog of the cover of a two-sphere by two planes. Using this covering he constructs line bundles over the quantum sphere and via an analog of the classical reduction using a polarization he arrives at irreducible representations on spaces of “holomorphic sections” of these bundles. Finally the classical limit of these constructions and possible generalizations are discussed.