How to create a circle icon button in Flutter?

How can I create something similar to a FloatingActionButton?

RawMaterialButton is better suited I think.

RawMaterialButton(
  onPressed: () {},
  elevation: 2.0,
  fillColor: Colors.white,
  child: Icon(
    Icons.pause,
    size: 35.0,
  ),
  padding: EdgeInsets.all(15.0),
  shape: CircleBorder(),
)

Update (use new ElevatedButton)

• ElevatedButton (with less customizations)

  ElevatedButton(
    onPressed: () {},
    child: Icon(Icons.menu, color: Colors.white),
    style: ElevatedButton.styleFrom(
      shape: CircleBorder(),
      padding: EdgeInsets.all(20),
      primary: Colors.blue, // <-- Button color
      onPrimary: Colors.red, // <-- Splash color
    ),
  )
  

• ElevatedButton (with more customizations)

  ElevatedButton(
    onPressed: () {},
    child: Icon(Icons.menu),
    style: ButtonStyle(
      shape: MaterialStateProperty.all(CircleBorder()),
      padding: MaterialStateProperty.all(EdgeInsets.all(20)),
      backgroundColor: MaterialStateProperty.all(Colors.blue), // <-- Button color
      overlayColor: MaterialStateProperty.resolveWith<Color?>((states) {
        if (states.contains(MaterialState.pressed)) return Colors.red; // <-- Splash color
      }),
    ),
  )
  

• Using InkWell

  ClipOval(
    child: Material(
      color: Colors.blue, // Button color
      child: InkWell(
        splashColor: Colors.red, // Splash color
        onTap: () {},
        child: SizedBox(width: 56, height: 56, child: Icon(Icons.menu)),
      ),
    ),
  )    
  

Output (same for the last two):

You just need to use the shape: CircleBorder()

MaterialButton(
  onPressed: () {},
  color: Colors.blue,
  textColor: Colors.white,
  child: Icon(
    Icons.camera_alt,
    size: 24,
  ),
  padding: EdgeInsets.all(16),
  shape: CircleBorder(),
)

You can use InkWell to do that:

A rectangular area of a Material that responds to touch.

Below example demonstrate how to use InkWell. Notice: you don't need StatefulWidget to do that. I used it to change the state of the count.

Example:

import 'package:flutter/material.dart';

class SettingPage extends StatefulWidget {
  @override
  _SettingPageState createState() => new _SettingPageState();
}

class _SettingPageState extends State<SettingPage> {
  int _count = 0;
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      body: new Center(
        child: new InkWell(// this is the one you are looking for..........
        onTap: () => setState(() => _count++),
        child: new Container(
          //width: 50.0,
          //height: 50.0,
          padding: const EdgeInsets.all(20.0),//I used some padding without fixed width and height
          decoration: new BoxDecoration(
            shape: BoxShape.circle,// You can use like this way or like the below line
            //borderRadius: new BorderRadius.circular(30.0),
            color: Colors.green,
          ),
          child: new Text(_count.toString(), style: new TextStyle(color: Colors.white, fontSize: 50.0)),// You can add a Icon instead of text also, like below.
          //child: new Icon(Icons.arrow_forward, size: 50.0, color: Colors.black38)),
        ),//............
      ),
      ),
    );
  }
}

If you want to get benefit of splashColor, highlightColor, wrap InkWell widget using a Material widget with material type circle. And then remove decoration in Container widget.

Outcome:

If you need a background image, you can use CircleAvatar with IconButton. Set the backgroundImage property.

CircleAvatar(
  backgroundImage: NetworkImage(userAvatarUrl),
)

Example with button:

        CircleAvatar(
          backgroundColor: Colors.blue,
          radius: 20,
          child: IconButton(
            padding: EdgeInsets.zero,
            icon: Icon(Icons.add),
            color: Colors.white,
            onPressed: () {},
          ),
        ),