We demonstrate a one to one correspondence between the polarization state of a light pulse tuned to excitonic resonances of single semiconductor quantum dots and the spin state of the exciton that it photogenerates. This is accomplished using two variably polarized and independently tuned picosecond laser pulses. The first “writes” the spin state of the resonantly excited exciton. The second is tuned to biexcitonic resonances, and its absorption is used to “read” the exciton spin state. The absorption of the second pulse depends on its polarization relative to the exciton spin direction. Changes in the exciton spin result in corresponding changes in the intensity of the photoluminescence from the biexciton lines which we monitor, obtaining thus a one to one mapping between any point on the Poincare sphere of the light polarization to a point on the Bloch sphere of the exciton spin.