In the general sense of the word, not in the sense that is meant by the more specific term "firearm registration".
No, it's not. There is no registration because there is no list of firearm owners matching them to the guns they own.
There are purchase records, distributed across the entire country, held primarily by FFLs.
Even the records held by the federal government are held in their original paper form, not compiled into a readily accessible list.
Even if the federal government were to collect all those records and compile them into a list (which would be illegal), they STILL wouldn't have a list of firearm owners and the guns they own because the records are purchase records, not ownership records.
Purchase records may relate person to guns they own in some cases, but in other cases they merely relate persons to purchased the guns, not necessarily to their current owners. As we should all know, there is no federal requirement for anyone to keep records when guns change hands within a given state between non-FFL holders.
I'm not saying it can't happen, it's just not happening now. It could happen, and here are a few of the things we would need to watch for.
1. New laws requiring that ALL firearm transactions must involve FFLs. This is one reason gun rights organizations are fighting so hard to protect gun shows. The push by anti-gunners to require ALL firearm transactions at gunshows (even those between two non-FFLs) go through FFLs can be seen as a first step towards registration.
2. Abolishment of existing laws preventing the BATF from collecting and compiling purchase records into a list of gun owners.
3. Laws requiring existing gun owners to compile and provide lists of the guns they own to the legal authorities.
It certainly could happen, but we're NOT there yet.