Hi,
ah, sorry, I misread the post, I was thinking about the normated spectra for earthquake as in the italian D.M. 14/09/05...
Yes, as Stringmaker says, if you have a time-dependent acceleration history, then you can perform a double integration. You will have only one "problem" in assigning appropriate values for the integration constants, but you can think about them as being initial velocity and displacement, so I believe you can fix it to zero.
But the time history is discrete, it's not written as a function, so you will have to make some assumption in re-building a piecewise function connecting groups of time points: the simplest is to connect only two successive time points in a linear fashion, so if you have n time points you will build n-1 functions of the type ai=mt+q, then you will pass to velocities vi=(1/2)mt^2+qt+c1 (where you can set c1=0 if you consider that the earthquake begins from a "stillstand" state), and lastly to displacements si=(1/6)mt^3+(1/2)qt^2+c1t+c2 (where you can drop the two last terms). The displacements have to be considered as "incremental": at time point t, the displacement s[t] is the sum of s[t-1] and si, and so on. It's tedious to do by hand, but almost immediate with Excel.
Hope this helps and that I didn't miss something...
Regards