A critical feature in signal processing is the ability to interpret correlations in time series signals, such as speech. Machine learning systems process this contextual information by tracking internal states in recurrent neural networks (RNNs), but these can cause memory and processor bottlenecks in applications from edge devices to data centers, motivating research into new analog inference architectures. But whereas photonic accelerators have demonstrated big leaps in uni-directional feedforward deep neural network (DNN) inference, the bi-directional architecture of RNNs presents a unique challenge: the need for a short-term memory that (i) programmably transforms optical waveforms with phase coherence , (ii) minimizes added noise, and (iii) enables programmable readily scales to large neuron counts. Here, we address this challenge by introducing an optoacoustic recurrent operator (OREO) that simultaneously meets (i,ii,iii). Specifically, we experimentally demonstrate an OREO that contextualizes and computes the information carried by a sequence of optical pulses via acoustic waves. We show that the acoustic waves act as a link between the different optical pulses, capturing the optical information and using it to manipulate the subsequent operations. Our approach can be controlled optically on a pulse-by-pulse basis, offering simple reconfigurability. We use this feature to demonstrate a recurrent drop-out, which excludes optical input pulses from the recurrent operation. We apply OREO as an acceptor to recognize up-to 27 patterns in a sequence of optical pulses. Finally, we introduce a DNN architecture that uses the OREO as bi-directional perceptrons to enable new classes of DNNs in coherent optical signal processing.