Coupling among closely packed waveguides is a common optical phenomenon, and plays an important role in optical routing and integration. Unfortunately, this coupling property is usually sensitive to the working wavelength and structure features that hinder the broadband and robust functions. Here, we report a new strategy utilizing an artificial gauge field (AGF) to engineer the coupling dispersion and realize a dispersionless coupling among waveguides with periodically bending modulation. The AGF-induced dispersionless coupling is experimentally verified in a silicon waveguide platform, which already has well-established broadband and robust routing functions (directional coupling and splitting), suggesting potential applications in integrated photonics. As examples, we further demonstrate a three-level-cascaded AGF waveguide network to route broadband light to desired ports with an overwhelming advantage over the conventional ones in comparison. Our method provides a new route of coupling dispersion control by AGF and benefits applications that fundamentally rely on waveguide coupling.