Yes, it is possible to manually connect AirPods to an iPhone. To do so, simply follow these steps:
1. Open the AirPods case and make sure they are charged and connected to the case.
2. On your iPhone, go to Settings > Bluetooth.
3. Make sure Bluetooth is turned on and then locate your AirPods under "My Devices".
4. Tap on your AirPods and wait for the iPhone to connect to them. You may be prompted to put them into your ears to complete the connection process.
5. Once connected, you should be able to use your AirPods to listen to music, make phone calls, and access Siri.
Note: If your AirPods are new and have never been connected to any device before, you may need to place them back in the case and hold the button on the back of the case until the LED light starts flashing. This will put your AirPods into pairing mode, allowing them to be discovered by your iPhone.