The best way to do this is to install a loopback network adapter and assign it the desired IP address. The machine will consider itself as "owning" that address, but it won't be visible on the actual network. For that matter, the machine won't even need to be connected to a real network.
You may have routing issues for the subnet surrounding the address you're hijacking by this method. This can be overcome by adding a persistent route for the affected subnet with a cheaper metric so that only the specific IP you want is routed to the loopback adapter, while the rest of that subnet is routed out to the real network.
You can also crank down the subnet mask so that only a handful of addresses are affected, for example using subnet mask 255.255.255.252 which will be a block of only 4 IP addresses. As long as your machine doesn't need to contact any outside hosts at any of those 4 IPs in the block, it will suffice without messing with persistent routes.
Oh, and of course you'll need your web server to be listening on that IP address. Setting it to listen on "all" addresses should suffice.