Is it possible to sort by a range in Elasticsearch?

It is not straight-forward to sort using a field of range data type. Still you can use script based sorting to some extent to get the expected result.

e.g. For simplicity of script I'm assuming for all your docs, the data indexed against my_range field has data for gt and lte only and you want to sort based on the minimum values of the two then you can add the below for sorting:

{
  "query": {
    "bool": {
      "filter": [
        {
          "match": {
            "my_value": "hi"
          }
        },
        {
          "range": {
            "my_range": {
              "gt": 0,
              "lte": 200
            }
          }
        }
      ]
    }
  },
  "sort": {
    "_script": {
      "type": "number",
      "script": {
        "lang": "painless",
        "inline": "Math.min(params['_source']['my_range']['gt'], params['_source']['my_range']['lte'])"            
      },
      "order": "asc"
    }
  }
}

You can modify the script as per your needs for complex data involving combination of all lt, gt, lte, gte.

Updates (Scripts for other different use cases):

1. Sort by difference

"Math.abs(params['_source']['my_range']['gt'] - params['_source']['my_range']['lte'])"

2. Sort by gt

"params['_source']['my_range']['gt']"

3. Sort by lte

"params['_source']['my_range']['lte']"

4. Sorting if query returns few docs which don't have range field

"if(params['_source']['my_range'] != null) { <sorting logic> } else { return 0; }"

Replace <sorting logic> with the required logic of sorting (which can be one of the 3 above or the one in the query)

return 0 can be replace by return -1 or anything other number as per the sorting needs