Can you apply for a visa for your spouse if you only have a green card?

As a permanent resident, you may apply for your spouse. It usually takes 2-4 years and if she is not in status while the case is pending, she will have to leave the US. But if you become a US citizen there will be no such problem. You may also talk to an immigration attorney about your citizenship. If one of your parents were a USC prior to your 18th birth day, you may be a US citizen already.

As you are a permanent resident, your wife is a 2nd preference relative, with a backlog of about 3 years. You should start the process by filing the relative petition (I-130) to get her a place in line for a green card. This date is called her "priority date". When the visas are available, she can then file for her green card if she is eligible. It is probably better for you to get your citizenship and then upgrade her case. She will be able to file immediately and her visa overstay and unauthorized employment is forgiven.

you can file I-130 but it will take 3-4 years. Even if the visa number becomes current, since she is out of status she may not adjust her status in the US. You should become US citizen as soon as you can. Or if your parents are US citizens, you may be US citizen already. Consult with immigration attorney.

When you become a USC, you can file for the green card right away, after having a full consult with a competent immigration attorney who ensures that your wife meets all eligibility requirements. Right now, you can file the first step of the process, the I-130 petition. IT takes currently about three years for her to then be able to file for a green card. However she will not be allowed to do that in the US unless you are a USC. And if she leaves to process, she will trigger a ten year bar. So be careful here and DO NOT do anything without a full consult!

Your wife could apply for a green card from within the U.S. since she entered on a visa. Although you could file an immigrant visa petition for your wife as a permanent resident, it will take approximately 3 years for her to take advantage of it and apply for adjustment of status (" green card"). Things would change if you became a U.S. citizen. Only then could your wife apply for adjustment right away. I recommend that you naturalize before you apply for her as she will not benefit from an application at this point.