Carbon microspheres with unusual magnetic properties have been prepared by the method of solid-phase pyrolysis where metal-free phthalocyanine was used as a precursor. The morphology, structure, and magnetic properties of prepared samples were investigated using electron microscopy, magnetometry, and electron paramagnetic resonance. Carbon microspheres with a mean diameter $d = 3.40\pm 0.15~\mu \text{m}$ consist of graphitized nanocrystallites with a thickness of 5–15 graphene layers. The samples demonstrate a strong paramagnetism with the concentration of paramagnetic centers $\sim 5\times 10^{19}$ spin/g. In the temperature range of 5–100 K, a ferromagnetism was revealed with a maximum value of the saturation magnetization, $ M_{s} \approx 0.03$ emu/g at $T= 25$ K. The temperature-independent diamagnetism with susceptibility of $\chi ^{\mathrm {Dia}}= -1 \,\, \times \,\, 10^{-6}$ emu/ $\textrm {g}\cdot \textrm {Oe}$ was also measured.