In this Letter, we numerically and experimentally demonstrate the carpet cloaking effect by a rectangular lattice two-dimensional photonic crystal (PC) exhibiting a semi-Dirac cone (SDC) dispersion phenomenon. The proposed SDC PC with an anisotropic zero refractive index medium operates as an optical carpet cloak for a perfect electric conductor surface bump. The experimental verification of the cloak is realized at microwave frequencies at around 12.1 GHz via dielectric rods. A good agreement between experimental measurements and numerical calculations is observed. Finally, features such as rendering larger objects invisible are possible with the proposed idea.