  We study the magnetic excitation spectra of Cu L_{2,3}-edge resonant
inelastic x-ray scattering (RIXS) from the spin-liquid ground state in two-leg
spin ladder cuprates. Applying the projection method developed by the present
authors, we have derived the formulas of the magnetic RIXS spectra, which are
expressed by one- and two-spin correlation functions in the polarization
changing and preserving channels, respectively. The one-spin correlation
function includes both one- and two-triplon excitations and they are picked up
separately by choosing rung wave vector -q_a=\pi and 0, respectively. An
application to Sr_{14}Cu_{24}O_{41} reveals that the calculated RIXS spectrum
captures well the dispersive behavior shown by the lower boundary of
two-triplon continuum. By adjusting the geometrical configuration of the
measurement, one-triplon dispersion around the zone center could be detectable
in the RIXS experiment. The observed weak intensity in the higher energy region
might be attributed to the two-spin correlation function, which could be
detected more clearly at the M_{3}-edge RIXS spectra.
