Index: src/wp-includes/rest-api/class-wp-rest-server.php
===================================================================
--- src/wp-includes/rest-api/class-wp-rest-server.php	(revision 37892)
+++ src/wp-includes/rest-api/class-wp-rest-server.php	(working copy)
@@ -228,6 +228,11 @@
 		$this->send_header( 'Content-Type', $content_type . '; charset=' . get_option( 'blog_charset' ) );
 		$this->send_header( 'X-Robots-Tag', 'noindex' );
 
+		$api_root = get_rest_url();
+		if ( ! empty( $api_root ) ) {
+			$this->send_header( 'Link', '<' . esc_url_raw( $api_root ) . '>; rel="https://api.w.org/"' );
+		}
+
 		/*
 		 * Mitigate possible JSONP Flash attacks.
 		 *
Index: tests/phpunit/tests/rest-api/rest-server.php
===================================================================
--- tests/phpunit/tests/rest-api/rest-server.php	(revision 37892)
+++ tests/phpunit/tests/rest-api/rest-server.php	(working copy)
@@ -726,6 +726,17 @@
 		$this->assertEquals( 'noindex', $headers['X-Robots-Tag'] );
 	}
 
+	public function test_link_header_on_requests() {
+		$api_root = get_rest_url();
+
+		$request = new WP_REST_Request( 'GET', '/', array() );
+
+		$result = $this->server->serve_request('/');
+		$headers = $this->server->sent_headers;
+
+		$this->assertEquals( '<' . esc_url_raw( $api_root ) . '>; rel="https://api.w.org/"', $headers['Link'] );
+	}
+
 	public function test_nocache_headers_on_authenticated_requests() {
 		$editor = self::factory()->user->create( array( 'role' => 'editor' ) );
 		$request = new WP_REST_Request( 'GET', '/', array() );