An asynchronous resampler should do the trick.
Basically positioning a continuous time windowed sinc at the desired (uniform) output time instants, sampling it by a neighbourhood of input time instants, choosing sinc width (inverse of bandwidth) either as a function of the largest input inter sample spacing, or locally as a function of sample density.
Unless sample density variation is large or quality requirements are really high, you can probably get by with something simpler. For some applications, simple linear interpolation could be sufficient. For high quality audio applications featuring tonal components, that may result in severe audible artifacts, but I struggle to imagine high quality audio applications where sample time is significantly variable?
A simple MATLAB code snippet that may do what you need would be this:
t1 = [0.000934,0.004197,0.005921,0.006978,0.007306,0.009449,0.012022,0.024245,0.030468,0.038149];
x1 = [0.446907,0.432984,0.410248,0.385579,0.363269,0.343606,0.328705,0.309281,0.285214,0.268380];
max_fs = 48e3;
fs = min(1/min(diff(t1)), max_fs);
[x2, t2] = resample(x1, t1, fs);
plot(t1, x1, '*')
plot(t2, x2, '-')
Note that I did not bother to dig into the documentation to see nitty gritty details. I confirmed that there is some shape similarity between input points and output points and assume the implementation to be sensible.