🎉 You can now, using React hooks

Using react hooks, you can now call useState() in your function component.

useState() will return an array of 2 things:

1. A value, representing the current state.
2. Its setter. Use it to update the value.

Updating the value by its setter will force your function component to re-render,
just like forceUpdate does:

import React, { useState } from 'react';

//create your forceUpdate hook
function useForceUpdate(){
    const [value, setValue] = useState(0); // integer state
    return () => setValue(value => value + 1); // update the state to force render
}

function MyComponent() {
    // call your hook here
    const forceUpdate = useForceUpdate();
    
    return (
        <div>
            {/*Clicking on the button will force to re-render like force update does */}
            <button onClick={forceUpdate}>
                Click to re-render
            </button>
        </div>
    );
}

You can find a demo here.

The component above uses a custom hook function (useForceUpdate) which uses the react state hook useState. It increments the component's state's value and thus tells React to re-render the component.

EDIT

In an old version of this answer, the snippet used a boolean value, and toggled it in forceUpdate(). Now that I've edited my answer, the snippet use a number rather than a boolean.

Why ? (you would ask me)

Because once it happened to me that my forceUpdate() was called twice subsequently from 2 different events, and thus it was reseting the boolean value at its original state, and the component never rendered.

This is because in the useState's setter (setValue here), React compare the previous state with the new one, and render only if the state is different.

Update react v16.8 (16 Feb 2019 realease)

Since react 16.8 released with hooks, function components are now have the ability to hold persistent state. With that ability you can now mimic a forceUpdate:

function App() {
  const [, updateState] = React.useState();
  const forceUpdate = React.useCallback(() => updateState({}), []);
  console.log("render");
  return (
    <div>
      <button onClick={forceUpdate}>Force Render</button>
    </div>
  );
}

const rootElement = document.getElementById("root");
ReactDOM.render(<App />, rootElement);

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.8.1/umd/react.production.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.8.1/umd/react-dom.production.min.js"></script>
<div id="root"/>

Note that this approach should be re-considered and in most cases when you need to force an update you probably doing something wrong.

Before react 16.8.0

No you can't, State-Less function components are just normal functions that returns jsx, you don't have any access to the React life cycle methods as you are not extending from the React.Component.

Think of function-component as the render method part of the class components.

Official FAQ ( https://reactjs.org/docs/hooks-faq.html#is-there-something-like-forceupdate ) now recommends this way if you really need to do it:

  const [ignored, forceUpdate] = useReducer(x => x + 1, 0);

  function handleClick() {
    forceUpdate();
  }