diff --git a/crates/accelerate/src/permutation.rs b/crates/accelerate/src/permutation.rs
index 31ba433ddd30..c4e5c649e6cd 100644
--- a/crates/accelerate/src/permutation.rs
+++ b/crates/accelerate/src/permutation.rs
@@ -14,8 +14,13 @@ use ndarray::{Array1, ArrayView1};
 use numpy::PyArrayLike1;
 use pyo3::exceptions::PyValueError;
 use pyo3::prelude::*;
+use smallvec::smallvec;
 use std::vec::Vec;
 
+use qiskit_circuit::circuit_data::CircuitData;
+use qiskit_circuit::operations::{Param, StandardGate};
+use qiskit_circuit::Qubit;
+
 fn validate_permutation(pattern: &ArrayView1<i64>) -> PyResult<()> {
     let n = pattern.len();
     let mut seen: Vec<bool> = vec![false; n];
@@ -111,10 +116,31 @@ fn _get_ordered_swap(py: Python, permutation_in: PyArrayLike1<i64>) -> PyResult<
     Ok(get_ordered_swap(&view).to_object(py))
 }
 
+#[pyfunction]
+#[pyo3(signature = (pattern))]
+fn _synth_permutation_basic(py: Python, pattern: PyArrayLike1<i64>) -> PyResult<CircuitData> {
+    let view = pattern.as_array();
+    let num_qubits = view.len();
+    Ok(CircuitData::from_standard_gates(
+        py,
+        num_qubits as u32,
+        get_ordered_swap(&view).iter().map(|(i, j)| {
+            (
+                StandardGate::SwapGate,
+                smallvec![],
+                smallvec![Qubit(*i as u32), Qubit(*j as u32)],
+            )
+        }),
+        Param::Float(0.0),
+    )
+    .expect("Something went wrong in Qiskit's Python realm"))
+}
+
 #[pymodule]
 pub fn permutation(m: &Bound<PyModule>) -> PyResult<()> {
     m.add_function(wrap_pyfunction!(_validate_permutation, m)?)?;
     m.add_function(wrap_pyfunction!(_inverse_pattern, m)?)?;
     m.add_function(wrap_pyfunction!(_get_ordered_swap, m)?)?;
+    m.add_function(wrap_pyfunction!(_synth_permutation_basic, m)?)?;
     Ok(())
 }
diff --git a/qiskit/synthesis/permutation/permutation_full.py b/qiskit/synthesis/permutation/permutation_full.py
index ff014cb3a051..9bbb75f925dc 100644
--- a/qiskit/synthesis/permutation/permutation_full.py
+++ b/qiskit/synthesis/permutation/permutation_full.py
@@ -16,8 +16,8 @@
 
 import numpy as np
 from qiskit.circuit.quantumcircuit import QuantumCircuit
+from qiskit._accelerate.permutation import _synth_permutation_basic
 from .permutation_utils import (
-    _get_ordered_swap,
     _inverse_pattern,
     _pattern_to_cycles,
     _decompose_cycles,
@@ -44,17 +44,7 @@ def synth_permutation_basic(pattern: list[int] | np.ndarray[int]) -> QuantumCirc
     Returns:
         The synthesized quantum circuit.
     """
-    # This is the very original Qiskit algorithm for synthesizing permutations.
-
-    num_qubits = len(pattern)
-    qc = QuantumCircuit(num_qubits)
-
-    swaps = _get_ordered_swap(pattern)
-
-    for swap in swaps:
-        qc.swap(swap[0], swap[1])
-
-    return qc
+    return QuantumCircuit._from_circuit_data(_synth_permutation_basic(pattern))
 
 
 def synth_permutation_acg(pattern: list[int] | np.ndarray[int]) -> QuantumCircuit:
diff --git a/releasenotes/notes/oxidize-permbasic-be27578187ac472f.yaml b/releasenotes/notes/oxidize-permbasic-be27578187ac472f.yaml
new file mode 100644
index 000000000000..e770aa1ca31b
--- /dev/null
+++ b/releasenotes/notes/oxidize-permbasic-be27578187ac472f.yaml
@@ -0,0 +1,4 @@
+---
+upgrade_synthesis:
+  - |
+    Port :func:`.synth_permutation_basic`, used to synthesize qubit permutations, to Rust.