Recent works have shown that modern machine learning techniques can provide an alternative approach to the long-standing joint source-channel coding (JSCC) problem. Very promising initial results, superior to popular digital schemes that utilize separate source and channel codes, have been demonstrated for wireless image and video transmission using deep neural networks (DNNs). However, end-to-end training of such schemes requires a differentiable channel input representation; hence, prior works have assumed that any complex value can be transmitted over the channel. This can prevent the application of these codes in scenarios where the hardware or protocol can only admit certain sets of channel inputs, prescribed by a digital constellation. Herein, we propose DeepJSCC-Q, an end-to-end optimized JSCC solution for wireless image transmission using a finite channel input alphabet. We show that DeepJSCC-Q can achieve similar performance to prior works that allow any complex valued channel input, especially when high modulation orders are available, and that the performance asymptotically approaches that of unconstrained channel input as the modulation order increases. Importantly, DeepJSCC-Q preserves the graceful degradation of image quality in unpredictable channel conditions, a desirable property for deployment in mobile systems with rapidly changing channel conditions.