signup.js

from django.test import import TestCase
from rest_framework import status
from rest_framework import APIClient

class SignupTestCase(TestCase):
  def setup():
    self.client = APIClient
    self.user = {
      "username":"username001",
      "email":"username001@example.com",
      "password":"password001"
    }
    def test_signup_new_user(self):
        """Test user registration"""
        response = self.client.post(
            '/api/signup',
            data=json.dumps(self.user),
            content_type="application/json")
        result = json.loads(response.data)
    self.assertEqual(self.response.status_code, status.HTTP_201_CREATED)

The tests are well written.
You may need to consider the indentation level for the second function.

I foresee a syntax error on the second function. Good job though!

make sure your doc strings are consistent.......you have not documented you, class.