Yes, you can. This is straight from Apple's Website:

You can use different Apple IDs for iCloud and store purchases and still get all of the benefits of iCloud. Just follow these steps:

iPhone, iPad, or iPod touch:


1. When you first set up your iOS 5 device, enter the Apple ID you want to use with iCloud. If you skipped the setup assistant, sign in to Settings > iCloud and enter the Apple ID you’d like to use with iCloud.
2. In Settings > Store, sign in with the Apple ID you want to use for store purchases (including iTunes in the Cloud and iTunes Match). You may need to sign out first to change the Apple ID.

Mac:

1. Enter the Apple ID you want to use for iCloud in Apple () menu > System Preferences > iCloud. 
2. Enter the Apple ID you want to use for store purchases (including iTunes in the Cloud and iTunes Match) iniTunes > iTunes Store

PC: 

1. Enter the Apple ID you want to use for iCloud in Control Panel > Network > Internet > iCloud. 
2. Enter the Apple ID you want to use for store purchases (including iTunes in the Cloud and iTunes Match) iniTunes > iTunes Store.

Note: You can switch the Apple ID you use for store purchases at any time. However, you can only change the account you use for any iTunes in the Cloud features once every 90 days. See this article for more information.