You can do this by adding the following code to the Header of your theme (or to the header of a theme component):
<script type="text/discourse-plugin" version="0.8">
const currentUser = api.getCurrentUser();
api.addPostClassesCallback((attrs) => {
if (currentUser && currentUser.id === attrs.user_id) {
return ["post-by-current-user"];
} else {
return [];
}
});
</script>
You can then use the post-by-current-user class in your stylesheet.