Accurately and rapidly classifying exoplanet candidates from transit surveys is a goal of growing importance as the data rates from space-based survey missions increases. This is especially true for NASAs TESS mission which generates thousands of new candidates each month. Here we created the first deep learning model capable of classifying TESS planet candidates. We adapted the neural network model of Ansdell et al. (2018) to TESS data. We then trained and tested this updated model on 4 sectors of high-fidelity, pixel-level simulations data created using the Lilith simulator and processed using the full TESS SPOC pipeline. We find our model performs very well on our simulated data, with 97% average precision and 92% accuracy on planets in the 2-class model. This accuracy is also boosted by another ~4% if planets found at the wrong periods are included. We also performed 3- and 4-class classification of planets, blended & target eclipsing binaries, and non-astrophysical false positives, which have slightly lower average precision and planet accuracies, but are useful for follow-up decisions. When applied to real TESS data, 61% of TCEs coincident with currently published TOIs are recovered as planets, 4% more are suggested to be EBs, and we propose a further 200 TCEs as planet candidates.