Follow procedure at https://www.linuxcapable.com/how-to-install-php-8-1-on-rocky-linux-9/

dnf config-manager --set-enabled crb
dnf install https://dl.fedoraproject.org/pub/epel/epel-release-latest-9.noarch.rpm 
dnf install https://dl.fedoraproject.org/pub/epel/epel-next-release-latest-9.noarch.rpm
dnf install dnf-utils http://rpms.remirepo.net/enterprise/remi-release-9.rpm
dnf remove php php-fpm
dnf remove php*
dnf module list reset php
dnf module list php
dnf module enable php:remi-8.1
dnf install php php-mbstring php-mysqlnd php-pecl-mcrypt php-pecl-mysql

Now check for installed version of PHP:

php -v

For issues running PHP, check Rocky Linux PHP 8.1 Upgrade for workarounds.