The Chi-squared goodness of fit test starts by binning data, then comparing the observed count in each bin to the theoretical or expected count. So if you can work out the number of points represented by each histogram bar and where the breaks are, then you have the input you need for the Chi-squared goodness of fit test. But note that the choices on how to bin a histogram can greatly influence perception. Look at @glen_b's answer to this question
Another approach is as described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
D.F and Wickham, H. (2009) Statistical Inference for exploratory
data analysis and model diagnostics Phil. Trans. R. Soc. A 2009
367, 4361-4383 doi: 10.1098/rsta.2009.0120
where you do a "line up" by generating several histograms of known normal data, but otherwise matching your histogram of interest (same breaks, sample size, etc.) then you present these normal histograms and your histogram to people not familiar with the original and see if they can pick out the one that is different from others. If everyone has an easy time picking out the original histogram then that would indicate that it is clearly not normal, but if people can't pick out the original then it is probably normal enough.
Of course, as Nick Stauner points out, most of the time normality testing is essentially useless, either giving a meaningless answer to a meaningful question, or a meaningful answer to a meaningless question.