Without relative motion or beam scanning, orbital-angular-momentum (OAM)-based radar is shown to be able to estimate azimuth of targets, which opens a new perspective for traditional radar techniques. However, the existing application of two-dimensional (2-D) fast Fourier transform (FFT) and multiple signal classification (MUSIC) algorithms in OAM-based radar targets detection doesn't realize 2-D super-resolution and robust estimation. Therefore, in this paper we propose a 2-D OAM radar targets detection method based on estimating signal parameter via rotational invariance (ESPRIT) algorithm. Our analysis and simulation results validate that OAM-based radar could achieve robust 2-D super-resolution imaging.