Optical vortex-arrays with multiple singularities have potential applications in high-capacity optical communication, particle manipulation and high-resolution measurement. Vortex-arrays with desirable spatial distribution of singularities and operating at new wavelengths further extend their applications. Here, an optical vortex-array with four singularities has been achieved in a Yb:YAG/YVO4 Raman microchip laser pumped with a tilted annular beam. Stable vortex-array with four singularities distributed in a square shape is achieved with simultaneous oscillation of frequency-degenerate modes in an asymmetric resonator with stimulated Raman scattering effect. Stable vortex-array with four singularities oscillates in a wide incident pump power (P-in) range from 2.8 to 5.7 W. The highest output power is 0.34 W with an optical efficiency of 5.9% for vortex-array with four-singularities at P-in = 5.7 W. The Raman laser oscillates in TEM00 mode at P-in < 2.8 W. Vortex-array with four singularities becomes unstable at P-in > 5.7 W and vortex-array with six singularities oscillates at P-in > 6 W. The highest Raman spectral width of vortex array laser is up to 16.8 nm, and 51 longitudinal modes oscillate. Inversion population is extremely important for stability of singularity-controllable Raman laser by transverse-mode locking, the experimental result is consistent with theory in transverse laser and interference pattern. This work of achieving vortex-array with transverse-mode locking creatively provides a compact Raman laser source, which endows more flexibilities in vortex laser applications.