Anti-jamming capability is of paramount importance in modern wireless communications, yet conventional receivers are severely constrained by their fixed array geometries, which limit the available spatial degrees of freedom and leave performance highly susceptible to strong interference. By contrast, movable antennas (MAs) provide additional spatial degrees of freedom through antenna-position optimization. This paper investigates MA-enabled anti-jamming by jointly optimizing the antenna-position vector (APV) and receive beamformer to maximize the output signal-to-interference-plus-noise ratio (SINR). For the canonical setting with a single jammer and a single line-of-sight (LoS) propagation path on the legitimate link, we develop a damped projected-gradient descent (DPGD) algorithm with low computational complexity, which scales linearly with the number of receive MAs. We establish a generic active strict-saddle landscape for the resulting steering-coherence minimization problem and prove that DPGD converges almost surely to a local minimizer rather than merely to a Karush-Kuhn-Tucker (KKT) point. For the general setting with multiple channel paths on the legitimate link and/or multiple jammers, we derive an equivalent ridge least-squares formulation and develop a low-complexity soft-active projected-gradient (SAPG) algorithm, which also scales linearly with the number of receive MAs. We further show that the proposed antenna position optimization framework applies to both minimum variance distortionless response (MVDR) and zero-forcing (ZF) reception. Numerical results validate the proposed algorithms, demonstrating substantial gains in both anti-jamming performance and computational efficiency.

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