A) To apply a static route on an ESXi host, effective immediately, but not persistent across a reboot:
Connect to host with a ssh client (I prefer putty) and execute the following command:

# route add -net <TargetNetwork> netmask <NetmaskAddress> gw <GatewayAddress> dev <interface>

e.g.

# route add -net 10.1.2.0 netmask 255.255.255.0 gw 10.1.1.1 dev eth0

then run

# route

to verify that the route was added successfully. In our example, the entry 10.1.2.0 10.1.1.1 255.255.255.0 UG 0 0 0 eth0 should appear.

B) To apply a persistent static route on the appliance:
Connect to host with a ssh client and open the static-routes file with a text editor:

# vi /etc/sysconfig/network/ifroute-eth0

(supposing the interface is eth0)
For every route add a line with the following format:

<TargetNetwork> <GatewayAddress> <Netmask> <Interface>

Then run the following command:

# service network restart

and finally verify the route with:

# route