Conventional social media platforms usually downscale high-resolution (HR) images to restrict their resolution to a specific size for saving transmission/storage cost, which makes those visual details inaccessible to other users. To bypass this obstacle, recent invertible image downscaling methods jointly model the downscaling/upscaling problems and achieve impressive performance. However, they only consider fixed integer scale factors and may be inapplicable to generic downscaling tasks towards resolution restriction as posed by social media platforms. In this paper, we propose an effective and universal Scale-Arbitrary Invertible Image Downscaling Network (AIDN), to downscale HR images with arbitrary scale factors in an invertible manner. Particularly, the HR information is embedded in the downscaled low-resolution (LR) counterparts in a nearly imperceptible form such that our AIDN can further restore the original HR images solely from the LR images. The key to supporting arbitrary scale factors is our proposed Conditional Resampling Module (CRM) that conditions the downscaling/upscaling kernels and sampling locations on both scale factors and image content. Extensive experimental results demonstrate that our AIDN achieves top performance for invertible downscaling with both arbitrary integer and non-integer scale factors. Also, both quantitative and qualitative evaluations show our AIDN is robust to the lossy image compression standard. The source code and trained models are publicly available at https://github.com/Doubiiu/AIDN.