How can I add an entity reference to a list entity refences of a node with rules?
You didn't post your setup and where you want to trigger the rule, but you would do this with PHP code added as a rule action:

$node = node_load(YOUR_NODE_ID);
$node-&gt;field_you_want_to_save[]['target_id'] = NEW_ENTITY_REFERENCE_ID;
$node-&gt;save();