diff --git a/diffcp/cone_program.py b/diffcp/cone_program.py
index f9b6f9a..40e0ade 100644
--- a/diffcp/cone_program.py
+++ b/diffcp/cone_program.py
@@ -10,6 +10,45 @@
 import diffcp.cones as cone_lib
 
 
+def permute_psd_rows(A: sparse.csc_matrix, b: np.ndarray, n: int, row_offset: int) -> sparse.csc_matrix:
+    """
+    Permutes rows of a sparse CSC constraint matrix A to switch from lower
+    triangular order (SCS) to upper triangular order (Clarabel) for a PSD constraint.
+
+    Args:
+        A (csc_matrix): Constraint matrix in CSC format.
+        n (int): Size of the PSD constraint matrix (n x n).
+        row_offset (int): Row index where the PSD block starts.
+
+    Returns:
+        csc_matrix: New CSC matrix with permuted rows.
+    """
+
+    tril_rows, tril_cols = np.tril_indices(n)
+    triu_rows, triu_cols = np.triu_indices(n)
+
+    # Compute the permutation mapping
+    tril_multi_index = np.ravel_multi_index((tril_cols, tril_rows), (n, n))
+    triu_multi_index = np.ravel_multi_index((triu_cols, triu_rows), (n, n))
+    postshuffle_from_preshuffle_perm = np.argsort(tril_multi_index) + row_offset
+    preshuffle_from_postshuffle_perm = np.argsort(triu_multi_index) + row_offset
+    n_rows = len(postshuffle_from_preshuffle_perm)
+
+    # Apply row permutation
+    data, rows, cols = A.data, A.indices, A.indptr
+    new_rows = np.copy(rows)  # Create a new row index array
+    # Identify affected rows
+    mask = (rows >= row_offset) & (rows < (row_offset + n_rows))
+    new_rows[mask] = postshuffle_from_preshuffle_perm[rows[mask] - row_offset]
+
+    new_A = sparse.csc_matrix((data, new_rows, cols), shape=A.shape)
+
+    new_b = np.copy(b)
+
+    new_b[row_offset:row_offset+n_rows] = new_b[preshuffle_from_postshuffle_perm]
+
+    return new_A, new_b
+
 def pi(z, cones):
     """Projection onto R^n x K^* x R_+
 
@@ -443,24 +482,33 @@ def solve_internal(A, b, c, cone_dict, solve_method=None,
         P = sparse.csc_matrix((c.size, c.size))
 
         cones = []
+        # Given the difference in convention between SCS (lower triangluar columnwise)
+        # and Clarabel (upper triangular columnwise), the rows of A may need to be permuted
+        start_row = 0
         if "z" in cone_dict:
             v = cone_dict["z"]
             if v > 0:
                 cones.append(clarabel.ZeroConeT(v))
+                start_row += v
         if "f" in cone_dict:
             v = cone_dict["f"]
             if v > 0:
                 cones.append(clarabel.ZeroConeT(v))
+                start_row += v
         if "l" in cone_dict:
             v = cone_dict["l"]
             if v > 0:
                 cones.append(clarabel.NonnegativeConeT(v))
+                start_row += v
         if "q" in cone_dict:
             for v in cone_dict["q"]:
                 cones.append(clarabel.SecondOrderConeT(v))
+                start_row += v
         if "s" in cone_dict:
             for v in cone_dict["s"]:
                 cones.append(clarabel.PSDTriangleConeT(v))
+                A, b = permute_psd_rows(A, b, v, start_row)
+                start_row += v
         if "ep" in cone_dict:
             v = cone_dict["ep"]
             cones += [clarabel.ExponentialConeT()] * v
diff --git a/pyproject.toml b/pyproject.toml
index 1cb177e..da92ba3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -8,6 +8,7 @@ requires-python = ">= 3.10"
 readme = "README.md"
 
 dependencies = [
+    "cvxpy>=1.6.3",
     "threadpoolctl >= 1.1",
 ]
 urls = {Homepage = "https://github.com/cvxgrp/diffcp/"}
@@ -31,7 +32,9 @@ test = [
     "clarabel >= 0.5.1",
     "ecos >= 2.0.10",
     "scs >= 3.0.0",
+    "pytest>=8.3.5",
 ]
 
 [tool.scikit-build]
 wheel.expand-macos-universal-tags = true
+
diff --git a/tests/test_clarabel.py b/tests/test_clarabel.py
index 822e5ce..c2f2046 100644
--- a/tests/test_clarabel.py
+++ b/tests/test_clarabel.py
@@ -2,6 +2,7 @@
 import numpy as np
 
 import diffcp.cone_program as cone_prog
+from diffcp.cones import unvec_symm
 import diffcp.utils as utils
 
 
@@ -120,3 +121,20 @@ def test_expcone():
         np.testing.assert_allclose(x_pert - x, dx, atol=1e-8)
         np.testing.assert_allclose(y_pert - y, dy, atol=1e-8)
         np.testing.assert_allclose(s_pert - s, ds, atol=1e-8)
+
+def test_psdcone():
+    DIM = 5
+    X = cp.Variable(shape=(DIM, DIM), PSD=True)
+    C = np.zeros((DIM, DIM))
+    C[0, 0] = 1
+    C[4, 4] = -1
+    objective = cp.Minimize(cp.trace(C @ X))
+    constraint = cp.trace(X) == 1
+    problem = cp.Problem(objective, [constraint])
+    A, b, c, cone_dims = utils.scs_data_from_cvxpy_problem(problem)
+    sol_vec, _, _, _, _ = cone_prog.solve_and_derivative(A, b, c, cone_dims, solve_method='Clarabel')
+
+    sol = unvec_symm(sol_vec, DIM)
+
+    assert np.abs(np.trace(sol) - 1.0) < 1e-6
+    assert (np.linalg.eigvals(sol) >= -1e-6).all()