Flow-based microfluidic biochips are promising with significant applications for automating and miniaturizing laboratory procedures in biochemistry. Automated design methods for flow-based microfluidic biochips are becoming increasingly important due to the advancement in both integration scale and design complexity for complicated biochemical applications. Though the multilayer soft lithography fabrication provides flexibility to route both flow and control channels in any angle, existing routing algorithms still adopt Manhattan routing metrics, which design channel in either vertical or horizontal direction only. Moreover, based on the computational fluid dynamics analysis, rectilinear channels with 90° bends have the following issues: 1) reduced the fluidic flow rate, which degrades the performance of the biochip and may even result in the erroneous outcome of the whole procedure and 2) increased pressure at the right-angle bend, which negatively affects the reliability of the biochip. To fully utilize the routing flexibility, this paper proposes the first any-angle routing algorithm for flow-based microfluidic biochip, called AARF. Computational simulation results show that compared with traditional Manhattan routing method, the proposed AARF significantly improves the total wirelength and total effective wirelength (considering the turning angles) by 17.11% and 35.91%, respectively, which prove the effectiveness of the AARF routing flow.