diff --git a/src/wp-includes/kses.php b/src/wp-includes/kses.php
index d1e3552f4e91b..bc6a98df6c564 100644
--- a/src/wp-includes/kses.php
+++ b/src/wp-includes/kses.php
@@ -2553,6 +2553,8 @@ function kses_init() {
  * @since 6.5.0 Added support for `background-repeat`.
  * @since 6.6.0 Added support for `grid-column`, `grid-row`, and `container-type`.
  * @since 6.9.0 Added support for `white-space`.
+ * @since 7.1.0 Added support for CSS anchor positioning properties and the
+ *              `anchor()` and `anchor-size()` functions.
  *
  * @param string $css        A string of CSS rules, decoded from an HTML `style` attribute.
  * @param string $deprecated Not used.
@@ -2734,6 +2736,16 @@ function safecss_filter_attr( $css, $deprecated = '' ) {
 			'aspect-ratio',
 			'container-type',
 
+			// CSS anchor positioning.
+			'anchor-name',
+			'anchor-scope',
+			'position-anchor',
+			'position-area',
+			'position-try',
+			'position-try-fallbacks',
+			'position-try-order',
+			'position-visibility',
+
 			'fill',
 			'fill-opacity',
 			'fill-rule',
@@ -2913,7 +2925,7 @@ function safecss_filter_attr( $css, $deprecated = '' ) {
 			 * Nested functions and parentheses are also removed, so long as the parentheses are balanced.
 			 */
 			$css_test_string = preg_replace(
-				'/\b(?:var|calc|min|max|minmax|clamp|repeat)(\((?:[^()]|(?1))*\))/',
+				'/\b(?:var|calc|min|max|minmax|clamp|repeat|anchor-size|anchor)(\((?:[^()]|(?1))*\))/',
 				'',
 				$css_test_string
 			);
diff --git a/tests/phpunit/tests/kses.php b/tests/phpunit/tests/kses.php
index 9ed3a45b2d90e..d3487fddbb7fd 100644
--- a/tests/phpunit/tests/kses.php
+++ b/tests/phpunit/tests/kses.php
@@ -1001,6 +1001,7 @@ public function test_wp_kses_attr_no_attributes_allowed_with_false() {
 	 * @ticket 60132
 	 * @ticket 64414
 	 * @ticket 65457
+	 * @ticket 64972
 	 *
 	 * @dataProvider data_safecss_filter_attr
 	 *
@@ -1511,6 +1512,31 @@ public function data_safecss_filter_attr() {
 				'css'      => 'text-anchor: middle',
 				'expected' => 'text-anchor: middle',
 			),
+			// CSS anchor positioning properties are allowed.
+			array(
+				'css'      => 'anchor-name: --tooltip;anchor-scope: all;position-anchor: --tooltip;position-area: top;position-try: flip-block;position-try-fallbacks: --fallback;position-try-order: most-height;position-visibility: anchors-visible',
+				'expected' => 'anchor-name: --tooltip;anchor-scope: all;position-anchor: --tooltip;position-area: top;position-try: flip-block;position-try-fallbacks: --fallback;position-try-order: most-height;position-visibility: anchors-visible',
+			),
+			// The `anchor()` function is allowed in inset properties.
+			array(
+				'css'      => 'top: anchor(--tooltip bottom)',
+				'expected' => 'top: anchor(--tooltip bottom)',
+			),
+			// The `anchor-size()` function is allowed in sizing properties.
+			array(
+				'css'      => 'width: anchor-size(--tooltip width)',
+				'expected' => 'width: anchor-size(--tooltip width)',
+			),
+			// The `anchor-size()` function is allowed when nested in another function.
+			array(
+				'css'      => 'margin-left: calc(anchor-size(width) / 2)',
+				'expected' => 'margin-left: calc(anchor-size(width) / 2)',
+			),
+			// Allowing `anchor()` must not allow other, unknown functions.
+			array(
+				'css'      => 'width: expression(alert(1))',
+				'expected' => '',
+			),
 		);
 	}