Yes you can.
On her iPad go to Settings>Messages>Send and Receive at>You can be reached for iMessage at>Uncheck your phone number. Then tap add another email address for your wife to use for Messages. I'm sure she has her own email address. Then let Apple verify the email address, check that as the email address that she uses for messages.
Take a look at his.
Either I missed it the first time around or you edited your post. Doesn't matter... If she wants to link her iPhone number to Messages look at this and read it all the way to the end.
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
Troubleshooting iMessage Issues: Some Useful Tips You Should Try
Setting Up Multiple iOS Devices for iMessage and Facetime
FaceTime and iMessage not accepting Apple ID password
Unable to use FaceTime and iMessage with my apple ID
How to Block Someone on FaceTime
My Facetime Doesn't Ring
For non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
How to Send SMS from iPad