I have documented this because I seem to need to do it every few months, and always seem to forgot exactly what has to be done for it to work (despite it being easy!). If you launch the VMware vSphere Web Client (https://vcenterhostname:9443/vsphere-client)
From the Web Client, click on Datacenters and then Hosts and expand the ESXi host that currently has the USB Disk attached.Select the VM you want to mount the USB Disk into and use the Edit... button to amend the VM Settings.
From the "Edit Settings" dialog box, use the New Device list to select USB Controller click Add to install this on the VM. Click OK to apply the settings.
Click Edit... again and use the New Device list again and this time select Host USB Device again use the Add button to install this on the VM. Click OK to apply the settings.
From the newly added Host USB Device list, the USB Disk should now appear in this list as an available disk. Select this from the list and click OK.
Although this was done inside the VMware vSphere Web Client, it can also be done in the traditional .NET based VMware Client.