The theoretical answer - no, unless you are in the Diplomatic Corps, or are moving to Nordrhein-Westphalia for only one year or are a military homeschooler under command sponsorship (although even this seems to jar with the regulations of at least one German state).
The practical answer - yes, and there are plenty of us who have managed to stay out of the gaze of the authorities, are are being tolerated by them, or have found some loophole in the law. Using a combination of these three strategies has enabled our family to homeschool in Germany for more than three years. The first possibility, escaping notice, is very often an option if your child is already of school age. If you have a child who is at the age where he/she would be starting school in September, you can forget about this, as the communities send the names of all these children who are registered with them to the relevant schools.
Some homeschooling families are lucky enough, that the local authorities tolerate them, even though they are theoretically in violation of the law and have no official exemption. This is even more likely to occur when the family in question is a foreign one, temporarily in Germany. There are those openminded school directors who have enough on their plates with running their own schools and see no purpose in hounding some family who aren't going to be in Germany long enough for their children to be integrated into the system. If the authorities are aware that you are there and your children are not attending school, it can really make a huge difference to your situation if you meet with the responsible school director and explain your situation in a friendly, open manner. Often their hands are tied, but if they are positively inclined towards you, they will do the very minimum that is necessary.
Sometimes it is worthwhile to examine the legal requirements and see if there are any legal loopholes that you can make use of. Sheila (my acting partner) seems to have found one which is working for her and her family, which involves living in Germany for nine months of the year (great excuse for a three-month vacation, Sheila). There are various other methods which have been used by homeschooling families, German as well as foreign, to keep the authorities off their back.
I've written this post because people have been coming to my blog as a result of searches like this. There is obviously a genuine (and hopefully growing) need for this kind of information.