The spectrum share and open nature of wireless channels enable integrated sensing and communication (ISAC) susceptible to hostile jamming attacks. Due to the intrinsic orthogonality and rich azimuth angle information of orbital angular momentum (OAM), vortex electromagnetic waves with helical phase fronts have shown great potential to achieve high-resolution imaging and strong anti-jamming capability of wireless communication. Focusing on significantly enhancing the anti-jamming results of ISAC systems with limited bandwidth under hostile jamming, in this paper we propose a novel ISAC for anti-jamming with OAM scheme, where the OAM legitimate transmitter can simultaneously sense the position of jammers with dynamic behavior and send data to multiple OAM legitimate users. Specifically, the OAM modes for sensing and communications are respectively hopped according to pre-set index modulation information to suppress jamming. To acquire the position of the jammer, we develop the enhanced multiple-signal-classification-based three-dimension position estimation scheme with continuous sensing in both frequency and angular domains, where the OAM transmitter is designed with the concentric uniform-circular-array mono-static method, to significantly increase the azimuthal resolution. Then, based on the acquired jamming channel state information, we develop the joint transmit-receive beamforming and power allocation scheme, where the transmit and receive beamforming matrices are dynamically adjusted to mitigate the mixed interference containing inter-mode interference, inter-user interference, and jamming, thus maximizing the achievable sum rates (ASRs) of all users. Numerical results demonstrate that our proposed scheme can significantly increase the ASR under broadband jamming attacks and achieve high detection accuracy of targets .