Magnetic properties of graphene nanostructures functionalized with aromatic radicals were investigated by electron spin resonance (ESR) and superconducting quantum interference device (SQUID) techniques. Three types of functionalized graphene samples were investigated (functionalization was performed by 4-bromoaniline, 4-nitroaniline, or 4-chloroaniline). According to SQUID measurements, in case of functionalization by nitroaniline, sharp change in temperature dependence of magnetic susceptibility was observed near 120 K. Such behavior was explained as antiferromagnetic ordering. The same but more extended effect was observed in ESR measurements below 160 K. In the ESR measurements, only one resonance line with -factor equal to 2.003 was observed. Based on the temperature dependencies of spin concentration and resonance position and intensity, the effect was explained as antiferromagnetic ordering along the extended defects on the basal planes of the graphene.