Android - Can we use an Android phone as a Wi-Fi repeater?

No. To do this would broadly speaking require multiple Wifi interfaces (or specialized software) which is not readily available (or easily installable) on Android.

In general this is done on Linux using something like hostapd in master mode: I don't believe that is easily setup on any Android phone.

The answer is yes, there is an open-source project available that does exactly that.

To quote:

It is a software designed to help you by-pass Great Firewall of China (GFW). Different from similar softwares, it is designed to run as router instead of running as a client installed on some device. Being router means, you can have one thing (Android mobile phone, for example) running fqrotuer, then other devices can just connect the wireless network created by fqrouter.

Blog: fqrouter Source: fqrouter

You should try Open Garden Wifi Tethering. It supports bluetooth, so You can easily share the connection this way. Of course, it would be slower, but still wireless. If You don't have bluetooth adapter, You can buy one on ebay for less than $2.