Added test following code review and generalized the change done in that commit.

theano/tensor/basic.py

@@ -4011,7 +4011,7 @@ class Join(Op):
             bcastable = [False] * len(as_tensor_variable_args[0].type.broadcastable)
             ndim = len(bcastable)
             # Axis can also be a constant
-            if isinstance(axis, Constant):
+            if not isinstance(axis, int):
                 try:
                     # Note : `get_constant_value` returns a ndarray not a
                     # int
@@ -5357,4 +5357,3 @@ def outer(x, y):
     return dot(
             x.dimshuffle(0, 'x'),
             y.dimshuffle('x', 0))
-

theano/tensor/tests/test_basic.py

@@ -2553,6 +2553,17 @@ class T_Join_and_Split(unittest.TestCase):
         assert c.type.broadcastable[0] and c.type.broadcastable[2]
         assert not c.type.broadcastable[1]
 
+        # Opt can remplace the int by a Theano constant
+        c = join(theano.tensor.constant(1), a, b)
+        assert c.type.broadcastable[0] and c.type.broadcastable[2]
+        assert not c.type.broadcastable[1]
+
+        # In case futur opt insert other useless stuff
+        c = join(theano.tensor.cast(theano.tensor.constant(1), dtype="int32"),
+                 a, b)
+        assert c.type.broadcastable[0] and c.type.broadcastable[2]
+        assert not c.type.broadcastable[1]
+
         f = function([a,b], c)
         rng = numpy.random.RandomState(seed=utt.fetch_seed())
         a_val = rng.rand(1, 4, 1).astype(config.floatX)