Use lsof to find the inode number, and debugfs to recreate a hard link to it. For example:
# lsof -p 12345 | grep /var/log/messages
syslogd 12345 root 3w REG 8,3 3000 987654 /var/log/messages (deleted)
# mount | grep var
/dev/sda2 on /var type ext3 (rw)
# debugfs -w /dev/sda2
debugfs: cd log
debugfs: ln <987654> tmp
debugfs: mi tmp
Mode [0100600]
User ID [0]
Group ID [0]
Size [3181271]
Creation time [1375916400]
Modification time [1375916322]
Access time [1375939901]
Deletion time [9601027] 0
Link count [0] 1
Block count [6232]
File flags [0x0]
...snip...
debugfs: q
# mv /var/log/tmp /var/log/messages
# ls -al /var/log/messages
-rw------- 0 root root 3301 Aug 8 10:10 /var/log/messages
Before you complain, I faked the above transcript as I don't have a deleted file to hand right now ;-)
I use mi to reset the delete time and link count to sensible values (0 and 1 respectively), but it doesn't work properly - you can see the link count remains at zero in ls. I think the kernel might be caching the inode data. You should probably fsck at the earliest opportunity after using debugfs, to be on the safe side.
In my experience, you should create the link using a temporary file name and then rename to the proper name. Linking it directly to the original file name seems to cause directory corruption. YMMV!