Transfer function estimation from logarithmic sweep frequency response data
Use FDLS (Frequency Domain Least Squares) to create a model of your measured frequency response. Use the frequency response of that model, evaluated at the FFT bin frequencies, as your filter. 

Alternate: if a low-order IIR (or perhaps even FIR) model provides a good-enough fit, then use the model as your filter for direct time-domain convolution.