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Simultaneous localization and mapping (SLAM) is a method that constructs a map of an unknown environment and localizes the position of a moving agent on the map simultaneously. Extended Kalman filter (EKF) has been widely adopted as a low complexity solution for online SLAM, which relies on a motion and measurement model of the moving agent. In practice, however, acquiring precise information about these models is very challenging, and the model mismatch effect causes severe performance loss in SLAM. In this paper, inspired by the recently proposed KalmanNet, we present a robust EKF algorithm using the power of deep learning for online SLAM, referred to as Split-KalmanNet. The key idea of Split-KalmanNet is to compute the Kalman gain using the Jacobian matrix of a measurement function and two recurrent neural networks (RNNs). The two RNNs independently learn the covariance matrices for a prior state estimate and the innovation from data. The proposed split structure in the computation of the Kalman gain allows to compensate for state and measurement model mismatch effects independently. Numerical simulation results verify that Split-KalmanNet outperforms the traditional EKF and the state-of-the-art KalmanNet algorithm in various model mismatch scenarios.