For self-driving cars, smartphones, and unmanned aerial vehicles (UAVs), cameras are typically used in combination with inertial measurement units (IMUs). The vertical direction of camera views can be determined based on partial IMU measurements, that is, the relative orientation of two views is reduced to a single degree of freedom. In this article, we propose a globally optimal solver using affine correspondences to estimate the relative pose of two views with a known vertical direction. First, the relative pose estimation problem is formalized as a cost function optimization, which minimizes algebraic error in the least-squares sense. Then, the cost function optimization is converted into two polynomials with only two unknowns, which are represented by the parameter of the rotation angle. Finally, we use the eigenvalue polynomial solver to calculate the parameter of the rotation angle. The proposed solver is evaluated using synthetic data and real-world scenes from the KITTI and EuRoC benchmarks. The experimental results show that our method performs better than existing state-of-the-art solvers.