Well, it's about 1 gauss!
But that doesn't get you very far, as the unit (the Gauss), named after the great German mathematician/stronomer/... was so defined that it matched the general strength of the Earth's magnetic field.
For what it's worth, the general magnetic field in the Sun's surface is also of order 1 gauss. However, in sunspots it reaches a strength of 1000's of gauss. THAT strength of field is sufficient to "split" atomic energy levels, removing a degeneracy that's there in the absence of a magnetic field. If one obtains a spectrum of part of the Sun's surface containing a strong sunspot, one can then directly observe the consequences of such "splitting" --- what would be single lines in the absence of a magnetic field may break up into 3, 5 etc. separate lines.
So, I suppose that you COULD define a magnetic field (and therefore the Earth's magnetic field) in terms of some fraction of what it would take to split some standard atomic line by some given measurable amount. However, unlike time (where the second is now defined with reference to the frequency of certain caesium lines), I don't think that hes ever been done, or maybe even suggested. (In which case, I'd like to have the credit for the idea!)
Live long and prosper.