This code allows you to implement reCAPTCHA by form

implement-recaptcha-by-form.php

<?php
/**
 * Implementing Google's ReCaptcha on specific GiveWP Forms
 *
 *  To effectively use this snippet, please do the following:
 *  1. Get your Google ReCAPTCHA API Key here: https://www.google.com/recaptcha/
 *  2. In each function and action, replace "_myprefix_" with your own custom prefix
 *  3. Put your "Secret Key" where it says "MYSECRETKEY" in the $recaptcha_secret_key string
 *  4. Put your "Site Key" where it says "MYSITEKEY" in TWO areas below
 */

/**
 * Validate ReCAPTCHA
 *
 * @param $valid_data
 * @param $data
 *
 * @return array $valid_data
 */
function give_myprefix_validate_recaptcha( $valid_data, $data ) {
	$recaptcha_url        = 'https://www.google.com/recaptcha/api/siteverify';
	$recaptcha_secret_key = 'MYSECRETKEY'; // Replace with your own key here.
	$recaptcha_response   = wp_remote_post( $recaptcha_url . '?secret=' . $recaptcha_secret_key . '&response=' . $data['g-recaptcha-response'] . '&remoteip=' . $_SERVER['REMOTE_ADDR'] );
	$recaptcha_data       = wp_remote_retrieve_body( $recaptcha_response );

	if ( ! isset( $recaptcha_data->success ) && ! $recaptcha_data->success == true ) {
		// User must have validated the reCAPTCHA to proceed with donation.
		if ( ! isset( $data['g-recaptcha-response'] ) || empty( $data['g-recaptcha-response'] ) ) {
			give_set_error( 'g-recaptcha-response', __( 'Please verify that you are not a robot.', 'give' ) );
		}
	}

	return $valid_data;
}

add_action( 'give_checkout_error_checks', 'give_myprefix_validate_recaptcha', 10, 2 );

/**
 * Print Necessary Inline JS for ReCAPTCHA
 *
 * This function outputs the appropriate inline js ReCAPTCHA scripts in the footer
 */
function give_myprefix_print_my_inline_script() {
	// Uncomment if statement to control output
	// if ( is_singular( 'give_forms' ) ) {
	?>
	<script type="text/javascript">
			jQuery( document ).on( 'give_gateway_loaded', function() {
				grecaptcha.render( 'give-recaptcha-element', {
					'sitekey': 'MYSITEKEY' // Add your own Google API sitekey here.
				} );
			} );
	</script>
	<?php
	// }
}

add_action( 'wp_footer', 'give_myprefix_print_my_inline_script' );

/**
 * Custom ReCAPTCHA Form Field
 *
 * This function adds the reCAPTCHA field above the "Donation Total" field.
 *
 * Don't forget to update the sitekey!
 *
 * @param $form_id
 */

function give_myprefix_custom_form_fields( $form_id ) {

	if( $form_id === 1234 ){
		wp_register_script( 'give-captcha-js', 'https://www.google.com/recaptcha/api.js' );		
		wp_enqueue_script( 'give-captcha-js' );
		add_action( 'wp_enqueue_scripts', 'give_myprefix_recaptcha_scripts' );

    // Add you own google API Site key.
	  ?>
	  <div id="give-recaptcha-element" class="g-recaptcha" data-sitekey="MYSITEKEY"
	       style="margin-bottom:1em"></div>
	  <?php }
}

add_action( 'give_donation_form_before_submit', 'give_myprefix_custom_form_fields', 10, 1 );