This feature is not currently available in Origin, but if one knows the algorithm it could be coded using either scripting or Origin C.
I did a breif search on geometric means regression and came up with this page (amongst many others): http://www.math.utah.edu/~zobitz/pdf_files/Spring05_teaching/matlab_assignment.pdf and according to this page, the GMR slope and intercept can be computed simply using the mean of X, Y data and the slope, intercept and correlation coefficient of the Least Square linear fit (that Origin performs). As for error estimates on the GMR paramters, and other things like how to incorporate x error bar if any etc, not sure...