In this paper, we propose an adaptive electro-optic equalizer for short-reach interconnects employing coherent modulation and detection. The equalizer consists of two main components: an optical equalizer filter and an electronic controller. The equalizer filter compensates for the linear dispersion occurring in the channel, while the electronic controller adaptively determines the weight coefficients of the equalizer. To achieve adaptive adjustment, we have introduced a random search algorithm. Extensive simulations have been conducted to evaluate the performance of the equalizer in a 120 Gbaud homodyne coherent link, and the results show great promise. The proposed equalizer has the potential to greatly improve the overall power efficiencies of receivers in short-reach coherent-lite interconnects.