Recent mobile devices are mostly integrated with cameras and accelerometer sensors. As long as the device is immobile, the accelerometer is affected just by gravity, hence the measured acceleration refers to gravity. On the other hand, synchronized captured images can also carry the direction of gravity information depending on the content of the scene. For instance, structures such as buildings, lighting poles, furniture, walls, and so on can show the direction of gravity in the images. These vertical structures in the image can be used to detect the vanishing point indicating the zenith. Hence, estimation of the camera internal parameters which map gravity vector into the vanishing point is possible. Based on this theory, in this work, we propose a novel camera calibration method that only requires taking photos of an arbitrary building and recording the synchronous acceleration vectors from an onboard accelerometer. Then, the vanishing points detected from the images and the acceleration vectors replace the 3-D calibrator. The resulting camera calibration method has competitive results compared to the popular calibrator-based methods despite it does not need any external calibrator object. The proposed camera calibration method both has the convenience of self-calibration approaches and gives highly competitive accuracy within calibrator-based approaches. The dataset and the code are available at https://github.com/okayarik/Camera-Calibration-Using-Accelerometer.