diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 370ea28832758..bc792713b5879 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -140,6 +140,7 @@ Other enhancements
 - :meth:`pandas.read_stata` and :class:`StataReader` support reading data from compressed files.
 - Add support for parsing ``ISO 8601``-like timestamps with negative signs to :meth:`pandas.Timedelta` (:issue:`37172`)
 - Add support for unary operators in :class:`FloatingArray` (:issue:`38749`)
+- :class:`RangeIndex` can now be constructed by passing a ``range`` object directly e.g. ``pd.RangeIndex(range(3))`` (:issue:`12067`)
 - :meth:`round` being enabled for the nullable integer and floating dtypes (:issue:`38844`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 09c143468bc31..23cb4d5df3f7b 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -366,16 +366,11 @@ def __new__(
         data_dtype = getattr(data, "dtype", None)
 
         # range
-        if isinstance(data, RangeIndex):
+        if isinstance(data, (range, RangeIndex)):
             result = RangeIndex(start=data, copy=copy, name=name)
             if dtype is not None:
                 return result.astype(dtype, copy=False)
             return result
-        elif isinstance(data, range):
-            result = RangeIndex.from_range(data, name=name)
-            if dtype is not None:
-                return result.astype(dtype, copy=False)
-            return result
 
         elif is_ea_or_datetimelike_dtype(dtype):
             # non-EA dtype indexes have special casting logic, so we punt here
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index bf5a9825f04d0..0c2d4a1872c98 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -116,7 +116,8 @@ def __new__(
 
         # RangeIndex
         if isinstance(start, RangeIndex):
-            start = start._range
+            return start.copy(name=name)
+        elif isinstance(start, range):
             return cls._simple_new(start, name=name)
 
         # validate the arguments
diff --git a/pandas/tests/indexes/ranges/test_constructors.py b/pandas/tests/indexes/ranges/test_constructors.py
index 599df3732a33b..9539b0ff7cdba 100644
--- a/pandas/tests/indexes/ranges/test_constructors.py
+++ b/pandas/tests/indexes/ranges/test_constructors.py
@@ -91,11 +91,12 @@ def test_constructor_same(self):
         ):
             RangeIndex(index, dtype="float64")
 
-    def test_constructor_range(self):
+    def test_constructor_range_object(self):
+        result = RangeIndex(range(1, 5, 2))
+        expected = RangeIndex(1, 5, 2)
+        tm.assert_index_equal(result, expected, exact=True)
 
-        msg = "Value needs to be a scalar value, was type range"
-        with pytest.raises(TypeError, match=msg):
-            result = RangeIndex(range(1, 5, 2))
+    def test_constructor_range(self):
 
         result = RangeIndex.from_range(range(1, 5, 2))
         expected = RangeIndex(1, 5, 2)