The central engine of gamma-ray bursts (GRBs) is poorly constrained. There exist two main candidates: a fast-rotating black hole and a rapidly spinning magnetar. Furthermore, X-ray plateaus are widely accepted to be the energy injection into the external shock. In this paper, we systematically analyze the Swift/XRT light curves of 101 GRBs having plateau phases and known redshifts (before 2017 May). Since a maximum energy budget (similar to 2 x 10(52) erg) exists for magnetars but not for black holes, this provides a good clue to identifying the type of GRB central engine. We calculate the isotropic kinetic energy E-K,(iso) and the isotropic X-ray energy release E-X,E-iso for individual GRBs. We identify three categories based on how likely a black hole harbors a central engine: Gold (9 out of 101; both E-X,E-iso and E-K,E-iso exceed the energy budget), Silver (69 out of 101; E-X,E-iso less than the limit but E-K,E-iso greater than the limit), and Bronze (23 out of 101; the energies are not above the limit). We then derive and test the black hole parameters with the Blandford-Znajek mechanism, and find that the observations of the black hole candidate (Gold + Silver) samples are consistent with the expectations of the black hole model. Furthermore, we also test the magnetar candidate (Bronze) sample with the magnetar model, and find that the magnetar surface magnetic field (B-p) and initial spin period (P-0) fall into reasonable ranges. Our analysis indicates that if the magnetar wind is isotropic, a magnetar central engine is possible for 20% of the analyzed GRBs. For most GRBs, a black hole is most likely operating.