This letter presents the first attempt of exploiting deep learning (DL) in the signal detection of orthogonal frequency division multiplexing with index modulation (OFDM-IM) systems. Particularly, we propose a novel DL-based detector termed as DeepIM, which employs a deep neural network with fully connected layers to recover data bits in an OFDM-IM system. To enhance the performance of DeepIM, the received signal and channel vectors are pre-processed based on the domain knowledge before entering the network. Using datasets collected by simulations, DeepIM is first trained offline to minimize the bit error rate (BER) and then the trained model is deployed for the online signal detection of OFDM-IM. Simulation results show that DeepIM can achieve a near-optimal BER with a lower runtime than existing hand-crafted detectors.