I am assuming that your spouse is a nonresident alien for tax purposes (the definitions of resident alien are really complicated, but it sounds likely that she is not).
In order to file as Married Filing Jointly, both people must be residents for tax purposes. So as your spouse is a nonresident, that means you must file as Married Filing Separately (or Head of Household if it applies). In the Form 1040 instructions, it says to put "NRA" in the space for SSN for the other spouse if they don't have one when filing separately.
There is an election you can do called Nonresident Spouse Treated as Resident. If the two of you make this election, your spouse will be treated as a resident alien for tax purposes, and you guys must file as Married Filing Jointly. Note that being a resident means that all her worldwide income is subject to U.S. taxes, but she may be able to reduce some or all of the U.S. taxes on her income using the Foreign Earned Income Exclusion (since she's not in the U.S. most of the year) and/or the Foreign Tax Credit (because she paid tax in her home country). Since she is not eligible for an SSN, she will apply for an ITIN (with Form W-7) at the same time as filing the tax return.