It looks like the endpoint / tags / tag-name will give you what you want:
Get information about the tag object.
Here is an example of them:
Request: https://api.instagram.com/v1/tags/nofilter?access_token=ACCESS-TOKEN
Answer:
{
"data": {
"media_count": 472,
"name": "nofilter",
}
}
[edit]
Just tested it with a pretty general tag ("cowboys"), and that was the answer:
{
"meta": {
"code": 200
},
"data": {
"media_count": 1195735,
"name": "cowboys"
}
}
~ 1,2 .