| Yes you can! (Providing you have Windows 7, excluding Windows 7 Starter Edition).
According to the faq for the Windows Upgrade Offer:
Do I have to install the Windows 8 upgrade on the eligible PC, or can I install it on another PC?
The upgrade offer is tied to a Windows 7 PC purchased between 2 June 2012 and 31 January 2013, but you can choose to redeem the offer and install the upgrade on any compatible Windows-based PC with a qualifying base operating system.
Are all PCs purchased with Windows 7 between 2 June 2012 and 31 January 2013 eligible for the Upgrade Offer?
Eligible PCs are new PCs purchased during the promotion period with a valid Windows 7 OEM Certificate of Authenticity, product key for and preinstalled with:
Windows 7 Home Basic;
Windows 7 Home Premium;
Windows 7 Professional; or
Windows 7 Ultimate
Note: Windows 7 Starter Edition is not eligible for this offer.