Not as a residential customer.
As a business customer you can have a static IP address (and pay the business rate, which also unblocks off network port 25 access)....
However for all practical purposes your FiOS IP address is static.
As long as the modem/router remains powered up and connected to the network, the lease will be renewed on time, and baring a change in the MAC address, the odds that you will keep the same IP address for a very long time (months to years) are surprisingly high.
There is no guarantee that you won't get a new IP address the next time you renew the lease, but the odds on it happening baring either event described above are very low.