I have an accelerometer on a table that gives me the $x$, $y$, and $z$ axis acceleration in $m/s^2$ when I move the table. Is there a formula or method to pass this data to a earthquake grade in a Richter Rank?
The Richter Number is a measure of total energy released in an earthquake. To calculate it, even roughly, you need to know the epicenter of the earthquake (that needs at least three measurements from three locations) and the length and intensity of the shaking to determine the energy contained in the waveform. All you seem to have with your accelerometer is the peak intensity of the shaking at a single point. So the answer is no.