You pass the geojson string directly to the ogr Open/gdal OpenEx function. 

In python it's just:

    #gdal 1.x
    ds = ogr.Open('some geojson string')

 or 

    #gdal 2.x
    ds = gdal.OpenEx('some geojson string')


An example to demonstrate:

    from osgeo import gdal
    
    geojson = '{"type":"FeatureCollection","features":[{"type":"Feature","properties":{},"geometry":{"type":"Point","coordinates":[146.7,-41.9]}}]}'
    ds = gdal.OpenEx(geojson)
    layer = ds.GetLayer()
    feature = layer.GetFeature(0)

    print(ds.GetDriver().ShortName)
    print(feature.GetGeometryRef().ExportToWkt())

Output:

    GeoJSON
    POINT (146.7 -41.9)