The ARIANNA experiment is a proposed Askaryan detector designed to record radio signals induced by neutrino interactions in the Antarctic ice. Because of the low neutrino flux at high energies, the physics output is limited by statistics. Hence, an increase in sensitivity significantly improves the interpretation of data and offers the ability to probe new parameter spaces. The trigger thresholds are limited by the rate of triggering on unavoidable thermal noise fluctuations. The real-time thermal noise rejection algorithm enables the thresholds to be lowered substantially and increases the sensitivity by up to a factor of two compared to the current ARIANNA capabilities. A deep learning discriminator, based on a Convolutional Neural Network (CNN), is implemented to identify and remove a high percentage of thermal events in real time while retaining most of the neutrino signals. We describe a CNN that runs on the current ARIANNA microcomputer and retains 95% of the neutrino signals at a thermal rejection factor of $10^5$. Finally, the experimental verification from lab measurements are conducted.