Hi! The game does have controller support. However, I believe it only natively supports d-input (not x-input).
There is a potential workaround, but I haven't tested it myself. You will need to go to Devices and Printers from the Windows Control Panel, right click your controller and select Game Controller Settings. From there, click Advanced, and set your preferred device to the same controller (it might already be set). After that, you'll need to rebind some keys. Click Properties, go to the Settings tab, then choose Calibrate. You will want to rebind X to A, B to B, A to Options, LB to Title Screen, and Analog Stick to up/down/left/right. Nothing else needs to be re-bound. I'm not sure if the d-pad is supported.