You can create an Azure VM on Azure, if more than one user will use the database try a D series VM (See the VM types here). After creating the VM, try to setup a VPN to connect to the VNET where Azure VM is deployed as explained here or you can try other ways to setup a VPN.
Put the MS access on a shared drive on the VM and once you are connected to the VNET of the Azure VM you should be able to access it.