The MaNGA project has obtained IFU data for several thousand nearby galaxies, including barred galaxies. With the two dimensional spectral and kinematic information provided by IFUs, we can measure the pattern speed of a barred galaxy, which determines the bar dynamics. We apply the non-parametric method proposed by Tremaine \& Weinberg to estimate the bar pattern speed for 53 barred galaxies, making this the largest sample studied so far in this way. Our sample is selected from the MaNGA first public data release as part of SDSS Data Release 13 according mainly to the axis ratio and position angle difference between the bar and disc, while kinematic data is from the later SDSS Data Release 14. We have used both the photometric position angle from the photometric image and the kinematic position angle from the stellar velocity map to derive the pattern speed. Combining three independent bar length measurements and the circular velocity from Jeans Anisotropic modelling (JAM), we also determine the dimensionless ratio R of the corotation radius to the bar length. We find that the galaxy's position angle is the main uncertainty in determining the bar pattern speed. The kinematic position angle leads to fewer ultrafast bars than the photometric position angle, and this could be due to the method of measuring the kinematic position angle. We study the dependence of R values on galaxy properties such as the dark matter fraction from JAM modelling and the stellar age and metallicity from stellar population synthesis (SPS). A positive correlation between the bar length and bar strength is found: the longer the bar, the stronger the bar. However, no other significant correlations are found. This may result from errors in deriving the R values or from the complex formation and slowdown processes of galactic bars.