Stellar feedback in dwarf galaxies plays a critical role in regulating star formation via galaxy-scale winds. Recent hydrodynamical zoom simulations of dwarf galaxies predict that the periodic outward flow of gas can change the gravitational potential sufficiently to cause radial migration of stars. To test the effect of bursty star formation on stellar migration, we examine star formation observables and sizes of 86 local dwarf galaxies. We find a correlation between the R-band half-light radius (R$_e$) and far-UV luminosity (L$_{FUV}$) for stellar masses below 10$^8 $ M$_{odot}$ and a weak correlation between the R$_e$ and H$alpha$ luminosity (L$_{Halpha}$). We produce mock observations of eight low-mass galaxies from the FIRE-2 cosmological simulations and measure the similarity of the time sequences of R$_e$ and a number of star formation indicators with different timescales. Major episodes of R$_e$ time sequence align very well with the major episodes of star formation, with a delay of $sim$ 50 Myrs. This correlation decreases towards SFR indicators of shorter timescales such that $R_e$ is weakly correlated with L$_{FUV}$ (10-100 Myr timescale) and is completely uncorrelated with L$_{Halpha}$ (a few Myr timescale), in agreement with the observations. Our findings based on FIRE-2 suggest that the R-band size of a galaxy reacts to star formation variations on a $sim50$ Myr timescale. With the advent of a new generation of large space telescopes (e.g., JWST), this effect can be examined explicitly in galaxies at higher redshifts where bursty star formation is more prominent.
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