If I take your question at face value I have to answer "NO" and say that there is no mapping of MAC address ==> IP address in the strictest sense of the wording. A MAC address is a hardware address usually assigned by a manufacturer (on some hardware you can set all or some of the MAC address in the field but I believe that has been depricated in most cases) and an IP address is assigned by a system or network administrator.

On the other hand, depending your OS you can to a very limited degree find a matching IP address for a given MAC and let me iterate some of the methods I would pursue:

ARP Caches

Mentioned elsewere in this thread is the concept of using an APR cache to lookup a hardware address and map it to an IP address. Let me look at two approaches for that:

Local ARP

On a *NIX system you can run a command called arp with the -a and it will dump the system's ARP cache to stdout. On my Linux box at home I get this kind of result from the command line:

$ /sbin/arp -a
router.isp.net  (168.239.116.1) at 00:01:5C:22:3C:42 [ether] on eth0
[download]

Note:IP addresses and names been changed to protect me!
If I wrte a Perl script to parse that I can map the ARP address  00:01:5C:22:3C:42 to it's associated IP address trivially.

The HUGE disadvantage this method has is only the ARP addresses for my local subnet are valid. If a host on the other side of the router from me then what is mapped into the ARP cache for a given IP address is the MAC address of the router. Not much help is it?

Other ARP caches

Another scheme would be to look at the ARP caches of every network device on my network and check it's ARP cache weeding out MAC addresses belonging to network devices.

In point of fact I wrote something called routerWalk several years ago that does just that. It logs onto the first router it sees, dumps its ARP cache, sifts through it and compares it to the routing table to determine which MAC addresses are valid and which belong to routers and stores the reesult. I wrote this in order to validate data stored in our IP Management system (QIP) and find unregistered hosts.

For that application that approach worked well but to do this every time you run a script that wants to reference that data would be impractical and a major PITA as well as not exactly a good way to make friends with your network operation folks.

Databases

Rarely actually populated but still do exist are the /etc/ethers files as well as the network distributed forms of them through NIS, NIS+ or whatever. If you have those available to you, use them.

In my environment I can actually query for that information against my QIP database and solve the problem that way.

Enjoy!