English does HAVE the glottal stop (ʔ), but it is not expressed by any alphabetic or punctuation marker.
For instance, most English-speaking people pronounce the interjection "uh-oh" with the glottal stop: uhʔ-oh.
Most Americans use the glottal stop (ʔ) in place of the final "t" sound in most words. For instance, "I'm not going" is typically pronounced as "I'm noʔ going."
However, again, the glottal stop is not actually present in the system, but is, rather, a matter of pronunciation (enunciation) only.