Short answer is yes but is very difficult to do. however, the reverse is easy.
--further clarification--
everything you do online leaves a digital footprint. without getting too technical here is how that can be done. Lets say time warner (TW)is your internet service provider. TW issues you an ip address via their DHCP server, that ip address is in their database as being assigned to your cable modem. Also in their database is the MAC address and an assigned hostname for your modem. so there, TW know who you are. Your use of an RFC 1918 ip address is irrelevant because those are not routable on the internet. therefore if you are using a router at home, even though your internal address would be part of the RFC 1918 space, it 192.168.x.x or 172.16.x.x or 10.x.x.x, the outside address TW assigns you is what will be used. In order to get to myspace or facebook you had to type the address in your browser which used the DNS server assigned by TW (you could use others) but the fact is there is a DNS record of your TW ip address requesting that address. so you get to facebook.com and create your account. The facebook servers time stamps when the account was created, login credentials, and the source, (your TW) ip address. As ROB mentions, ISP rotate ip addresses, but it is unclear how long the keep track of what address is assigned to what users. Most have some sort of policy that is used by law enforcement. sophisticated hackers know how to hid their addresses but even that is not fool proof.
Answered May 18, 2013
Edited May 18, 2013