If BOTH spouses want to file jointly, you can file a Joint return.  But the spouse will need to apply for an ITIN.

Although an ITIN can be applied for when filing the tax return (by postal mail), the optimal way to get an ITIN is through a Certifying Acceptance Agent or at an IRS Center (so after they get the ITIN, you could hypothetically e-file, *IF* the IRS computers are updated with the ITIN).

https://www.irs.gov/individuals/how-do-i-apply-for-an-itin

ITIN is not a standalone application. As a Certifying Acceptance Agent (CAA), I submit both the ITIN application and tax return to the ITIN office in Austin, TX. After the ITIN is issued, the personnel at the ITIN office will inscribe the ITIN on your tax return. They then forward it to another department for processing. You typically cannot e-file your federal return in the year you apply for an ITIN unless you needed an ITIN for other reason than filing a tax return. However, you can E-file your state return after getting ITIN, and e-filing will be available to you from the following year onward. 

Did you mean your client is married to a resident alien (Green Card holder)?  If so, the spouse should be eligible to apply for SSN at Social Security Administration.