We observed HCO$^+$ $J=1-0$ and H$^{13}$CO$^+$ $J=1-0$ emission towards the five protoplanetary disks around IM Lup, GM Aur, AS 209, HD 163296, and MWC 480 as part of the MAPS project. HCO$^+$ is detected and mapped at 0.3arcsec,resolution in all five disks, while H$^{13}$CO$^+$ is detected (SNR$>6 sigma$) towards GM Aur and HD 163296 and tentatively detected (SNR$>3 sigma$) towards the other disks by a matched filter analysis. Inside a radius of $Rsim 100$ au, the HCO$^+$ column density is flat or shows a central dip. At outer radii ($gtrsim 100$ au), the HCO$^+$ column density decreases outwards, while the column density ratio of HCO$^+$/CO is mostly in the range of $sim 10^{-5}-10^{-4}$. We derived the HCO$^+$ abundance in the warm CO-rich layer, where HCO$^+$ is expected to be the dominant molecular ion. At $Rgtrsim 100$ au, the HCO$^+$ abundance is $sim 3 times 10^{-11} - 3times 10^{-10}$, which is consistent with a template disk model with X-ray ionization. At the smaller radii, the abundance decreases inwards, which indicates that the ionization degree is lower in denser gas, especially inside the CO snow line, where the CO-rich layer is in the midplane. Comparison of template disk models with the column densities of HCO$^+$, N$_2$H$^+$, and N$_2$D$^+$ indicates that the midplane ionization rate is $gtrsim 10^{-18}$ s$^{-1}$ for the disks around IM Lup, AS 209, and HD 163296. We also find hints of an increased HCO$^+$ abundance around the location of dust continuum gaps in AS 209, HD 163296, and MWC 480. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.
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