how can i add_option as array from a form with just a text input

Something like this should work.

function si_ad_call_models() {

    if ( isset( $_POST['submit'] ) ) {

        // Checking that $_POST['new_model_name'] is set is probably not enough validation.
        if ( isset( $_POST['new_model_name'] ) ) {

            // Get the stored models.
            if ( get_option( 'si_ad_call_model' ) )
                $si_ad_call_models = unserialize( get_option( 'si_ad_call_model' ) );

            else
                $si_ad_call_models = array();

            // Add the new model to the end of the models array.
            // @TODO Clean $_POST['new_model_name'] before adding it to database.
            $si_ad_call_models[] = $_POST['new_model_name'];

            // Store the updated array of models.
            if ( update_option( 'si_ad_call_model', serialize( $si_ad_call_models ) ) ) {
                // @TODO Tell user about success.

            } else {
                // @TODO Tell user about failure.
                // @TODO Log database update failure.
            }

        } else {
            // @TODO Add validation error code.
        }
    }

    // Title of the page.
    echo '<h2>Add new ad call model</h2>';
?>
    <form action="" method="post">
        <label for="add">Enter name of ad model: </label>
        <input type="text" name="new_model_name"/>
        <input type="submit" name="submit" value="Add your new ad model"/>
    </form>
<?php
}

I did not fully test this code.