diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index b4d1787697973..103008f4a7c8c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -516,7 +516,7 @@ ExtensionArray
 - Fixed Bug where :class:`DataFrame` column set to scalar extension type via a dict instantion was considered an object type rather than the extension type (:issue:`35965`)
 - Fixed bug where ``astype()`` with equal dtype and ``copy=False`` would return a new object (:issue:`284881`)
 - Fixed bug when applying a NumPy ufunc with multiple outputs to a :class:`pandas.arrays.IntegerArray` returning None (:issue:`36913`)
-
+- Fixed an inconsistency in :class:`PeriodArray`'s ``__init__`` signature to those of :class:`DatetimeArray` and :class:`TimedeltaArray` (:issue:`37289`)
 
 Other
 ^^^^^
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index bf2b3a0a1c9ba..ba2048a496ef8 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -76,14 +76,14 @@ class PeriodArray(PeriodMixin, dtl.DatelikeOps):
         converted to ordinals without inference or copy (PeriodArray,
         ndarray[int64]), or a box around such an array (Series[period],
         PeriodIndex).
+    dtype : PeriodDtype, optional
+        A PeriodDtype instance from which to extract a `freq`. If both
+        `freq` and `dtype` are specified, then the frequencies must match.
     freq : str or DateOffset
         The `freq` to use for the array. Mostly applicable when `values`
         is an ndarray of integers, when `freq` is required. When `values`
         is a PeriodArray (or box around), it's checked that ``values.freq``
         matches `freq`.
-    dtype : PeriodDtype, optional
-        A PeriodDtype instance from which to extract a `freq`. If both
-        `freq` and `dtype` are specified, then the frequencies must match.
     copy : bool, default False
         Whether to copy the ordinals before storing.
 
@@ -148,7 +148,7 @@ class PeriodArray(PeriodMixin, dtl.DatelikeOps):
     # --------------------------------------------------------------------
     # Constructors
 
-    def __init__(self, values, freq=None, dtype=None, copy=False):
+    def __init__(self, values, dtype=None, freq=None, copy=False):
         freq = validate_dtype_freq(dtype, freq)
 
         if freq is not None:
@@ -882,7 +882,7 @@ def period_array(
     if is_datetime64_dtype(data_dtype):
         return PeriodArray._from_datetime64(data, freq)
     if is_period_dtype(data_dtype):
-        return PeriodArray(data, freq)
+        return PeriodArray(data, freq=freq)
 
     # other iterable of some kind
     if not isinstance(data, (np.ndarray, list, tuple, ABCSeries)):
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 4f92bb7bd7a87..41968c5972ea5 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -214,7 +214,7 @@ def __new__(
             if data is None and ordinal is not None:
                 # we strangely ignore `ordinal` if data is passed.
                 ordinal = np.asarray(ordinal, dtype=np.int64)
-                data = PeriodArray(ordinal, freq)
+                data = PeriodArray(ordinal, freq=freq)
             else:
                 # don't pass copy here, since we copy later.
                 data = period_array(data=data, freq=freq)