We present a quasi-Monte Carlo acceptance-rejection sampling method for arbitrary multivariate continuous probability density functions. The method employs either a uniform or a Gaussian proposal distribution. The proposal samples are provided by optimal deterministic sampling based on the generalized Fibonacci lattice. By using low-discrepancy samples from generalized Fibonacci lattices, we achieve a more locally homogeneous sample distribution than random sampling methods for arbitrary continuous densities such as the Metropolis-Hastings algorithm or slice sampling, or acceptance-rejection based on state-of-the-art quasi-random sampling methods like the Sobol or Halton sequence.