Это должно сделать это:
NSString *title = @"\n\n\n\n\n\n\n\n\n\n\n\n"; // <--- Taken from Erica Sadun´s CookBook
UIActionSheet *actionSheet = [[UIActionSheet alloc] initWithTitle:title delegate:self cancelButtonTitle:nil destructiveButtonTitle:nil otherButtonTitles: nil];
[actionSheet setActionSheetStyle:UIActionSheetStyleBlackTranslucent];
[actionSheet setBounds:CGRectMake(0,0,320,485)];
UIPickerView *picker = [[UIPickerView alloc] initWithFrame:CGRectMake(0, 0, 320, 216)];
[picker setDataSource:self];
[picker setDelegate:self];
[picker setShowsSelectionIndicator:YES];
[actionSheet addSubview:picker];
[actionSheet showFromTabBar:[[self tabBarController] tabBar]];
Пожалуйста, помните, что вы должны установить источник данных UIPickerView и делегировать.