カテゴリで実装していますが、
ViewControllerであればコピペで使えるレベルです。

実装

UIViewController+Alert.m

#import "UIViewController+Alert.h"

@implementation UIViewController (Alert)

- (void)showIndicatorAlert:(NSString*)text
{
    UIAlertController *alertController = [UIAlertController alertControllerWithTitle:@"" message:text preferredStyle:UIAlertControllerStyleAlert];
    UIActivityIndicatorView *view = [[UIActivityIndicatorView alloc] initWithActivityIndicatorStyle:UIActivityIndicatorViewStyleGray];
    view.center = CGPointMake(60, 30);
    [alertController.view addSubview:view];
    [view startAnimating];
    [self presentViewController:alertController animated:YES completion:nil];
}

@end

呼び出し元


[self showIndicatorAlert:@"Please wait..."];

表示結果

閉じる方法

別スレッドとかで


... 処理 ...

// 閉じる
dispatch_sync(dispatch_get_main_queue(), ^{
    [self dismissViewControllerAnimated:true completion:nil];
});

Swift版

extension UIViewController {
    func showIndicatorAlert(text: String) {
        let alert = UIAlertController(title: text,
                                      message: "",
                                      preferredStyle: .alert)
        let indicatorView = UIActivityIndicatorView(style: .medium)
        indicatorView.center = CGPoint(x: 60, y: 30)
        indicatorView.startAnimating()
        alert.view.addSubview(indicatorView)
        self.present(alert, animated: true, completion: nil)
    }
}

表示

self.showIndicatorAlert(text: "Please wait...")

閉じる

self.dismiss(animated: true)