If the Canadian national you married is a Nonresident Alien, you may elect to file Married Filing Jointly or file Married Filing Separately, but in either case, your spouse will need a Social Security number or an ITIN if you are going to file electronically. 

If you have a dependent, you may be able to file Head Of Household, which would free you from the obligation of obtaining an ITIN or SS number for your spouse. See more here.

If you are unable to get a Social Security number or ITIN for your spouse, you will need to enter a fake number in the Taxpayer Identification Number (TIN) box and then print out and mail the return. You will need to whiteout the fake number you entered, replacing that with the letters NRA in the TIN box. 

There is an excellent page of information from the IRS here. There is more information about Taxpayer Identification Numbers (like SS and ITIN numbers) here.

Thank you! She has 2 children from a previous marriage, however they both live in Canada on a split custody basis. I do not have any children/dependents living with me or otherwise. Does this preclude me from filing single, head of household? 

If you do not have a dependent who you can claim as a Qualifying Child, then you can not file as Head of Household.

This leaves Married Filing Jointly or Married Filing Separately. Because the US taxes worldwide income, Married Filing Jointly might be complicated. If you formally filed single with few or no credits you may not notice the difference (besides potentially mailing the forms in).