  The absolute differential cross section for small-angle proton elastic
scattering on the proton-rich $^8$B nucleus has been measured in inverse
kinematics for the first time. The experiment was performed using a secondary
radioactive beam with an energy of 0.7 GeV/u at GSI, Darmstadt. The active
target, namely hydrogen-filled time projection ionization chamber IKAR, was
used to measure the energy, angle and vertex point of the recoil protons. The
scattering angle of the projectiles was simultaneously determined by the
tracking detectors. The measured differential cross section is analyzed on the
basis of the Glauber multiple scattering theory using phenomenological
nuclear-density distributions with two free parameters. The radial density
distribution deduced for $^8$B exhibits a halo structure with the
root-mean-square (rms) matter radius $R_{\rm m} = 2.58 (6)$ fm and the rms halo
radius $R_{\rm h} = 4.24 (25)$ fm. The results on $^8$B are compared to those
on the mirror nucleus $^8$Li investigated earlier by the same method. A
comparison is also made with previous experimental results and theoretical
predictions for both nuclei.
