Add custom input to digits form

Paste code into your theme functions.php. I hope it's working on the registration form.

functions.php

// Displaying the field
function wp_registration_form() {
    $year = ! empty( $_POST['year_of_birth'] ) ? intval( $_POST['year_of_birth'] ) : '';
    ?>
    <p>
        <label for="year_of_birth"><?php esc_html_e( 'Year of birth', 'wp' ) ?><br/>
            <input type="number" min="1900" max="2017" step="1" id="year_of_birth" name="year_of_birth" value="<?php echo esc_attr( $year ); ?>"class="input"/>
        </label>
    </p>
    <?php
}
add_action( 'register_form', 'wp_registration_form' );

// Validating the field
function wp_registration_errors( $errors, $sanitized_user_login, $user_email ) {

    if ( empty( $_POST['year_of_birth'] ) ) {
        $errors->add( 'year_of_birth_error', __( '<strong>ERROR</strong>: Please enter your year of birth.', 'wp' ) );
    }

    if ( ! empty( $_POST['year_of_birth'] ) && intval( $_POST['year_of_birth'] ) < 1900 ) {
        $errors->add( 'year_of_birth_error', __( '<strong>ERROR</strong>: You must be born after 1900.', 'wp' ) );
    }

    return $errors;
}
add_filter( 'registration_errors', 'wp_registration_errors', 10, 3 );

// Sanitizing and saving the field
function wp_user_register( $user_id ) {
    if ( ! empty( $_POST['year_of_birth'] ) ) {
        update_user_meta( $user_id, 'year_of_birth', intval( $_POST['year_of_birth'] ) );
    }
}
add_action( 'user_register', 'wp_user_register' );

/**
 * Back end registration
 */

function wp_admin_registration_form( $operation ) {
    if ( 'add-new-user' !== $operation ) {
        // $operation may also be 'add-existing-user'
        return;
    }

    $year = ! empty( $_POST['year_of_birth'] ) ? intval( $_POST['year_of_birth'] ) : '';

    ?>
    <h3><?php esc_html_e( 'Personal Information', 'wp' ); ?></h3>

    <table class="form-table">
        <tr>
            <th><label for="year_of_birth"><?php esc_html_e( 'Year of birth', 'wp' ); ?></label> <span class="description"><?php esc_html_e( '(required)', 'wp' ); ?></span></th>
            <td>
                <input type="number"
                   min="1900"
                   max="2017"
                   step="1"
                   id="year_of_birth"
                   name="year_of_birth"
                   value="<?php echo esc_attr( $year ); ?>"
                   class="regular-text"
                />
            </td>
        </tr>
    </table>
    <?php
}
add_action( 'user_new_form', 'wp_admin_registration_form' );

// Validating the field
function wp_user_profile_update_errors( $errors, $update, $user ) {
    if ( $update ) {
        return;
    }

    if ( empty( $_POST['year_of_birth'] ) ) {
        $errors->add( 'year_of_birth_error', __( '<strong>ERROR</strong>: Please enter your year of birth.', 'wp' ) );
    }

    if ( ! empty( $_POST['year_of_birth'] ) && intval( $_POST['year_of_birth'] ) < 1900 ) {
        $errors->add( 'year_of_birth_error', __( '<strong>ERROR</strong>: You must be born after 1900.', 'wp' ) );
    }
}
add_action( 'user_profile_update_errors', 'wp_user_profile_update_errors', 10, 3 );
add_action( 'edit_user_created_user', 'wp_user_register' );

// Profile display
function wp_show_extra_profile_fields( $user ) {
    ?>
    <h3><?php esc_html_e( 'Personal Information', 'wp' ); ?></h3>

    <table class="form-table">
        <tr>
            <th><label for="year_of_birth"><?php esc_html_e( 'Year of birth', 'wp' ); ?></label></th>
            <td><?php echo esc_html( get_the_author_meta( 'year_of_birth', $user->ID ) ); ?></td>
        </tr>
    </table>
    <?php
}
add_action( 'show_user_profile', 'wp_show_extra_profile_fields' );
add_action( 'edit_user_profile', 'wp_show_extra_profile_fields' );

Output screen: