You can json_encode() it which will make it a string that you can put into a custom field then just ensure you json_decode() it to bring it back to an object or json_decode($data, true) to bring it back as an array
$arr = array("Accounting"=>"Peter", "Finance"=>"Ben", "Marketing"=>"Joe");
update_post_meta($post_id, "my_custom_meta_key", json_encode($arr));
$json_data = get_post_meta($post_id, "my_custom_meta_key", true); // true to ensure it comes back as a string and not an array
$arr_data = json_decode($json_data, true); // 2nd parameter == true so it comes back as an array();