$objectManager = MagentoFrameworkAppObjectManager::getInstance();
$cart = $objectManager->get('MagentoCheckoutModelCart');
$salesRuleFactory = $objectManager->get('MagentoSalesRuleModelRuleFactory');
$salesRule = $salesRuleFactory->create();
$salesRuleId = 2;
$salesRule->load($salesRuleId);
$couponCode = $salesRule->getPrimaryCoupon()->getCode();

$cart->getQuote()->setCouponCode(trim($couponCode));
$cart->getQuote()->collectTotals()->save();