One of the main challenges in orthogonal frequency division multiplexing (OFDM)-subcarrier index modulation (SIM) systems is the huge amount of resources required to obtain channel state information at the receiver side. In this paper, a differential subcarrier index modulation (DSIM) scheme is proposed, which entirely avoids the need for any channel knowledge at the receiver side. As such, time and energy resources spent in the channel estimation process are perceived. In DSIM, part of the transmitted block is modulated through ordinary signal modulation, whereas the second part is transmitted by selecting a specific permutation of the active subcarriers. The transmitted signals are designed to facilitate differential demodulation at the receiver side. A derivation is conducted for the average bit error probability of DSIM and an upper bound expression is obtained. Derived theoretical expression is substantiated through Monte Carlo simulation results. Reported results reveal that differential demodulation degrades the error performance of coherent SIM by nearly 4 dB in signal-to-noise-ratio.