Drought is a frequent and costly natural disaster in California, with major negative impacts on agricultural production and water resource availability, particularly groundwater. This study investigated the performance of applying different machine learning approaches to predicting the U.S. Drought Monitor classification in California. Four approaches were used: a convolutional neural network (CNN), random forest, XGBoost, and long short term memory (LSTM) recurrent neural network, and compared to a baseline persistence model. We evaluated the models' performance in predicting severe drought (USDM drought category D2 or higher) using a macro F1 binary classification metric. The LSTM model emerged as the top performer, followed by XGBoost, CNN, and random forest. Further evaluation of our results at the county level suggested that the LSTM model would perform best in counties with more consistent drought patterns and where severe drought was more common, and the LSTM model would perform worse where drought scores increased rapidly. Utilizing 30 weeks of historical data, the LSTM model successfully forecasted drought scores for a 12-week period with a Mean Absolute Error (MAE) of 0.33, equivalent to less than half a drought category on a scale of 0 to 5. Additionally, the LSTM achieved a macro F1 score of 0.9, indicating high accuracy in binary classification for severe drought conditions. Evaluation of different window and future horizon sizes in weeks suggested that at least 24 weeks of data would result in the best performance, with best performance for shorter horizon sizes, particularly less than eight weeks.