On-chip focusing of plasmons in graded-index lenses is important for imaging, lithography, signal processing, and optical interconnects at the deep subwavelength nanoscale. However, owing to the inherent strong wavelength dispersion of plasmonic materials, the on-chip focusing of plasmons suffers from severe chromatic aberrations. With the well-established planar dielectric grating, a graded-index waveguide array lens (GIWAL) is proposed to support the excitation and propagation of acoustic graphene plasmon polaritons (AGPPs) and to achieve the achromatic on-chip focusing of the AGPPs with a focus as small as about 2% of the operating wavelength in the frequency band from 10 to 20 THz, benefiting from the wavelength-independent index profile of the GIWAL. An analytical theory is provided to understand the on-chip focusing of the AGPPs and other beam evolution behaviors, such as self-focusing, self-collimation, and pendulum effects of Gaussian beams as well as spatial inversions of digital optical signals. Furthermore, the possibility of the GIWAL to invert spatially broadband digital optical signals is demonstrated, indicating the potential value of the GIWAL in broadband digital communication and signal processing.