diff --git a/airflow-core/src/airflow/config_templates/config.yml b/airflow-core/src/airflow/config_templates/config.yml
index 33d52dfe75a84..b718e36e7235e 100644
--- a/airflow-core/src/airflow/config_templates/config.yml
+++ b/airflow-core/src/airflow/config_templates/config.yml
@@ -1403,6 +1403,8 @@ api:
       description: |
         Paths to the SSL certificate and key for the api server. When both are
         provided SSL will be enabled. This does not change the api server port.
+        The same SSL certificate will also be loaded into the worker to enable
+        it to be trusted when a self-signed certificate is used.
       version_added: ~
       type: string
       example: ~
diff --git a/task-sdk/src/airflow/sdk/api/client.py b/task-sdk/src/airflow/sdk/api/client.py
index 36489d3d79d58..3413e98189cfc 100644
--- a/task-sdk/src/airflow/sdk/api/client.py
+++ b/task-sdk/src/airflow/sdk/api/client.py
@@ -18,11 +18,13 @@
 from __future__ import annotations
 
 import logging
+import ssl
 import sys
 import uuid
 from http import HTTPStatus
 from typing import TYPE_CHECKING, Any, TypeVar
 
+import certifi
 import httpx
 import msgspec
 import structlog
@@ -660,6 +662,7 @@ def noop_handler(request: httpx.Request) -> httpx.Response:
 API_RETRIES = conf.getint("workers", "execution_api_retries")
 API_RETRY_WAIT_MIN = conf.getfloat("workers", "execution_api_retry_wait_min")
 API_RETRY_WAIT_MAX = conf.getfloat("workers", "execution_api_retry_wait_max")
+API_SSL_CERT_PATH = conf.get("api", "ssl_cert")
 
 
 class Client(httpx.Client):
@@ -675,6 +678,10 @@ def __init__(self, *, base_url: str | None, dry_run: bool = False, token: str, *
             kwargs.setdefault("base_url", "dry-run://server")
         else:
             kwargs["base_url"] = base_url
+            ctx = ssl.create_default_context(cafile=certifi.where())
+            if API_SSL_CERT_PATH:
+                ctx.load_verify_locations(API_SSL_CERT_PATH)
+            kwargs["verify"] = ctx
         pyver = f"{'.'.join(map(str, sys.version_info[:3]))}"
         super().__init__(
             auth=auth,
diff --git a/task-sdk/tests/task_sdk/api/test_client.py b/task-sdk/tests/task_sdk/api/test_client.py
index 7fa17ba1c4d38..caa515de09a4d 100644
--- a/task-sdk/tests/task_sdk/api/test_client.py
+++ b/task-sdk/tests/task_sdk/api/test_client.py
@@ -79,6 +79,16 @@ def test_dry_run(self, path, json_response):
         assert resp.status_code == 200
         assert resp.json() == json_response
 
+    @mock.patch("airflow.sdk.api.client.API_SSL_CERT_PATH", "/capath/does/not/exist/")
+    def test_add_capath(self):
+        def handle_request(request: httpx.Request) -> httpx.Response:
+            return httpx.Response(status_code=200)
+
+        with pytest.raises(FileNotFoundError) as err:
+            make_client(httpx.MockTransport(handle_request))
+
+        assert isinstance(err.value, FileNotFoundError)
+
     def test_error_parsing(self):
         responses = [
             httpx.Response(422, json={"detail": [{"loc": ["#0"], "msg": "err", "type": "required"}]})