Higher magic angle spinning (MAS) frequencies than currently available are desirable to improve spectral resolution in NMR and EPR systems. While conventional strategies employ pneumatic spinning limited by fluid dynamics, this paper demonstrates the development of an optical spinning technique in which vacuum quality dictates the maximum achievable spinning frequency. Using optical traps, we levitated a range of micron-sized samples. Under vacuum we achieved optical rotation of a single 10 mu m diameter particle of vaterite at several mbar up to hundreds of Hz and of 20 mu m diameter SiO2 particles at <= 10(- 2) mbar at several kHz. At ambient conditions, we optically levitated gamma-irradiated alanine particles of 20-50 mu m diameter. Additionally, using a single chip EPR detector operating at 11 GHz, we measured the EPR spectrum for a 30 mu m gamma-irradiated alanine particle in contact with the chip surface (i.e., without optical levitation) in a single scan lasting 92 s. These observations suggest that a gamma-irradiated alanine particle having a diameter in the order of 30 mu m is a promising candidate for our aim of demonstrating the first magnetic resonance experiment on optically levitated samples. Furthermore, we discuss strategies, limitations, and the potential of implementing MAS with optical traps for NMR and EPR.