Radio-frequency (RF) front-end forms a critical part of any radio system, defining its cost as well as communication performance. However, these components frequently exhibit non-ideal behavior, referred to as impairments, due to the imperfections in the manufacturing/design process. Most of the designers rely on simplified closed-form models to estimate these impairments. On the other hand, these models do not holistically or accurately capture the effects of real-world RF front-end components. Recently, machine learning-based algorithms have been proposed to estimate these impairments. However, these algorithms are not capable of estimating multiple RF impairments jointly, which leads to limited estimation accuracy. In this paper, the joint estimation of multiple RF impairments by exploiting the relationship between them is proposed. To do this, a deep multi-task learning-based algorithm is designed. Extensive simulation results reveal that the performance of the proposed joint RF impairments estimation algorithm is superior to the conventional individual estimations in terms of mean-square error. Moreover, the proposed algorithm removes the need of training multiple models for estimating the different impairments.