The gravimeter inclination is a significant parameter for cold atom gravimeters, and the counter-propagating Raman beams should be exactly parallel to the local vector of gravity. The tiltmeters, essential devices in cold atom gravimeters, are used to determine the optimum inclination of Raman beams and compensate for the inclination error. However, the conventional tiltmeters may lead to system errors in cold atom gravimeters due to insufficient nonlinearity and drift. In this study, we establish an optical interferometer inside the cold atom gravimeter by placing a hollow beam splitter plate in the path of the Raman beams. This optical interferometer as a tiltmeter to measure the inclination change of the Raman beams without influencing the gravity measurement. We prove that our optical tiltmeter (OT) works well with field assembly. Comparisons of our OT and commercial tiltmeters reveal that the nonlinearity of our OT is at least one-tenth of that of the commercial tiltmeters, and that the drift of our OT is at least 23 $\upmu$rad less than that of the commercial tiltmeters over 90 h measurements. This can reduce a typical value of atom gravimeters system error by 4 $\upmu$Gal. Further, a comparison of measured gravity to inclination deviation calibrated our OT and further validated that our OT outperforms commercial tiltmeters. This work enables more precise measurement of Raman beam angle variations and facilitates the calibration of installed tiltmeters, whether in the laboratory and the field.