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)
feature.GetGeometryRef().ExportToWkt()
print(ds.GetDriver().ShortName)
print(feature.GetGeometryRef().ExportToWkt())
Output:
GeoJSON
POINT (146.7 -41.9)