We report the experimentally determined oscillator strengths for the 5s6s 1S0→5snp 1P1 Rydberg transitions of strontium using two-step excitation in conjunction with a thermionic diode ion detector. The absolute photoionization cross section from the 5s6s 1S0 excited state has been determined by adjusting the polarization vector of the ionizing laser beam parallel, perpendicular, and at the magic angle with respect to that of the exciting dye laser. The measured absolute value of the photoionization cross section 0.9±0.2 Mb at the 5s threshold is used to extract the f values of the 5s6s 1S0→5snp 1P1 (26≤n≤73) Rydberg transitions. The oscillator strength in the discrete region merges smoothly to the oscillator strength density at the ionization threshold.