diff --git a/changelog.d/12944.misc b/changelog.d/12944.misc
new file mode 100644
index 000000000..bf27fe7e2
--- /dev/null
+++ b/changelog.d/12944.misc
@@ -0,0 +1 @@
+Add `Cross-Origin-Resource-Policy: cross-origin` header to content repository's thumbnail and download endpoints.
\ No newline at end of file
diff --git a/synapse/http/server.py b/synapse/http/server.py
index e3dcc3f3d..cf2d6f904 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -928,6 +928,17 @@ def set_cors_headers(request: Request) -> None:
     )
 
 
+def set_corp_headers(request: Request) -> None:
+    """Set the CORP headers so that javascript running in a web browsers can
+    embed the resource returned from this request when their client requires
+    the `Cross-Origin-Embedder-Policy: require-corp` header.
+
+    Args:
+        request: The http request to add the CORP header to.
+    """
+    request.setHeader(b"Cross-Origin-Resource-Policy", b"cross-origin")
+
+
 def respond_with_html(request: Request, code: int, html: str) -> None:
     """
     Wraps `respond_with_html_bytes` by first encoding HTML from a str to UTF-8 bytes.
diff --git a/synapse/rest/media/v1/download_resource.py b/synapse/rest/media/v1/download_resource.py
index 6180fa575..048a04269 100644
--- a/synapse/rest/media/v1/download_resource.py
+++ b/synapse/rest/media/v1/download_resource.py
@@ -15,7 +15,11 @@
 import logging
 from typing import TYPE_CHECKING
 
-from synapse.http.server import DirectServeJsonResource, set_cors_headers
+from synapse.http.server import (
+    DirectServeJsonResource,
+    set_corp_headers,
+    set_cors_headers,
+)
 from synapse.http.servlet import parse_boolean
 from synapse.http.site import SynapseRequest
 
@@ -38,6 +42,7 @@ class DownloadResource(DirectServeJsonResource):
 
     async def _async_render_GET(self, request: SynapseRequest) -> None:
         set_cors_headers(request)
+        set_corp_headers(request)
         request.setHeader(
             b"Content-Security-Policy",
             b"sandbox;"
diff --git a/synapse/rest/media/v1/thumbnail_resource.py b/synapse/rest/media/v1/thumbnail_resource.py
index 53b156524..2295adfaa 100644
--- a/synapse/rest/media/v1/thumbnail_resource.py
+++ b/synapse/rest/media/v1/thumbnail_resource.py
@@ -18,7 +18,11 @@ import logging
 from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple
 
 from synapse.api.errors import SynapseError
-from synapse.http.server import DirectServeJsonResource, set_cors_headers
+from synapse.http.server import (
+    DirectServeJsonResource,
+    set_corp_headers,
+    set_cors_headers,
+)
 from synapse.http.servlet import parse_integer, parse_string
 from synapse.http.site import SynapseRequest
 from synapse.rest.media.v1.media_storage import MediaStorage
@@ -58,6 +62,7 @@ class ThumbnailResource(DirectServeJsonResource):
 
     async def _async_render_GET(self, request: SynapseRequest) -> None:
         set_cors_headers(request)
+        set_corp_headers(request)
         server_name, media_id, _ = parse_media_id(request)
         width = parse_integer(request, "width", required=True)
         height = parse_integer(request, "height", required=True)
diff --git a/tests/rest/media/v1/test_media_storage.py b/tests/rest/media/v1/test_media_storage.py
index 7204b2dfe..1c67e1ca9 100644
--- a/tests/rest/media/v1/test_media_storage.py
+++ b/tests/rest/media/v1/test_media_storage.py
@@ -481,6 +481,12 @@ class MediaRepoTests(unittest.HomeserverTestCase):
 
         if expected_found:
             self.assertEqual(channel.code, 200)
+
+            self.assertEqual(
+                channel.headers.getRawHeaders(b"Cross-Origin-Resource-Policy"),
+                [b"cross-origin"],
+            )
+
             if expected_body is not None:
                 self.assertEqual(
                     channel.result["body"], expected_body, channel.result["body"]
@@ -549,6 +555,20 @@ class MediaRepoTests(unittest.HomeserverTestCase):
             [b"noindex, nofollow, noarchive, noimageindex"],
         )
 
+    def test_cross_origin_resource_policy_header(self) -> None:
+        """
+        Test that the Cross-Origin-Resource-Policy header is set to "cross-origin"
+        allowing web clients to embed media from the downloads API.
+        """
+        channel = self._req(b"inline; filename=out" + self.test_image.extension)
+
+        headers = channel.headers
+
+        self.assertEqual(
+            headers.getRawHeaders(b"Cross-Origin-Resource-Policy"),
+            [b"cross-origin"],
+        )
+
 
 class TestSpamChecker:
     """A spam checker module that rejects all media that includes the bytes