The answer, in a nutshell, is of course a single parent can home school. It just might take more time management and coordinated logistics than a stay-at-home parent with spousal support. As one single parent who has and does home school (not all my children all the time, I admit), I can testify that it can be done, it just takes some focus, planning, and flexibility.
The age of the child will have a direct impact on how you can go about home schooling. A younger, elementary-age child will need much more direct supervision and guidance than an older teenager or high school-age child. Keep in mind that you do not have to be responsible for everything yourself (like most things having to do with single parenting–we think we have to be the only resource, but there are other people and organizations out there to help us.) Consider joining a home schooling association and connecting with other parents in your area. Be on the look-out for other single parents who are home schooling as they will be able to share direct experience about how to juggle, manage, and educate.
It may help to write out a schedule so you can actually see how you will fit in “school” with your work and other obligations. There is no set rule that says school has to happen between the hours of 9 am and 3 pm. Home schooling means that you can find the optimum time for both you and your child for doing school work. You can usually have time that you spend with the child, teaching, and he or she can work on his own too. If you have to work outside the home (and most of us do), you can make other activity arrangements during your working hours. Perhaps the child can take an art class, or a reading group, or do an activity with other home schooled children. You may also be able to enlist the help of a retired grandparent or friend to help with home schooling while you are working.
As long as you use your community resources, and help your child experience plenty of opportunities for socialization, there is no reason that a single parent cannot also be a home schooling parent.
See Also: Homeschooling Blog