How can I make rounded TextField in flutter?

You can try this code bellow:

      decoration:  InputDecoration(
         border: OutlineInputBorder(
             borderRadius: const BorderRadius.all(
                const Radius.circular(10.0), 
             ),
             borderSide: BorderSide(
              width: 0, 
              style: BorderStyle.none,
              ),
             ),
           )

@Rockvole answer is correct but just in case u don't like the default border around the TextField, you can achieve it by overriding the borderSide attribute of the OutlineInputBorder like this:

TextField(
    textAlign: TextAlign.center,
    controller: searchCtrl,
    keyboardType: TextInputType.text,
    decoration: InputDecoration(
        hintText: 'Enter a product name eg. pension',
        hintStyle: TextStyle(fontSize: 16),
        border: OutlineInputBorder(
            borderRadius: BorderRadius.circular(8),
            borderSide: BorderSide(
                width: 0, 
                style: BorderStyle.none,
            ),
        ),
        filled: true,
        contentPadding: EdgeInsets.all(16),
        fillColor: colorSearchBg,
    ),
),

You can get desired output with the help of Container Have a look..

new Container(
  child: new Text (
      "Text with rounded edges.",
      style: new TextStyle(
          color: Colors.blue[500],
          fontWeight: FontWeight.w900
      )
  ),
  decoration: new BoxDecoration (
      borderRadius: new BorderRadius.all(new Radius.circular(10.0)),
      color: Colors.black
  ),
  padding: new EdgeInsets.fromLTRB(16.0, 16.0, 16.0, 16.0),
),

You can add rounded corners to a TextField within the decoration parameter of it

TextField(
  decoration: InputDecoration(
      border: OutlineInputBorder(
        borderRadius: BorderRadius.circular(10.0),
      ),
      filled: true,
      hintStyle: TextStyle(color: Colors.grey[800]),
      hintText: "Type in your text",
      fillColor: Colors.white70),
)