Artistic style transfer is the task of synthesizing content images with learned artistic styles. Recent studies have shown the potential of Generative Adversarial Networks (GANs) for producing artistically rich stylizations. Despite the promising results, they usually fail to control the generated images' style degree, which is inflexible and limits their applicability for practical use. To address the issue, in this paper, we propose a novel method that for the first time allows adjusting the style degree for existing GAN-based artistic style transfer frameworks in real time after training. Our method introduces two novel modules into existing GAN-based artistic style transfer frameworks: a Style Scaling Injection (SSI) module and a Style Degree Interpretation (SDI) module. The SSI module accepts the value of Style Degree Factor (SDF) as the input and outputs parameters that scale the feature activations in existing models, offering control signals to alter the style degrees of the stylizations. And the SDI module interprets the output probabilities of a multi-scale content-style binary classifier as the style degrees, providing a mechanism to parameterize the style degree of the stylizations. Moreover, we show that after training our method can enable existing GAN-based frameworks to produce over-stylizations. The proposed method can facilitate many existing GAN-based artistic style transfer frameworks with marginal extra training overheads and modifications. Extensive qualitative evaluations on two typical GAN-based style transfer models demonstrate the effectiveness of the proposed method for gaining style degree control for them.