Yes. WordPress websites are responsive, but not all. The responsive capability of a WordPress website depends on the theme and the plugins that you are using. Let's take a look at how your choice of theme and plugins can effect the overall responsiveness of your website.
WordPress themes define your websites front-end design look and feel, from navigation layouts and logo positions to content styling and the overall structure of your blog posts. Changing themes will change how your content displays to your visitors, including the display on mobile devices. It is important when choosing a theme to check if it advertises a responsive design layout.
WordPress plugins can add additional functionality to a website that is not offered by a theme. Plugins that display content such as page builders and sliders, may affect the overall responsive nature of your website. For example the SiteOrigin Hero Slider that forms part of the Widgets Bundle plugin, scales both the image and overlay text to suit all mobile devices.
Responsive Web Design
With more people accessing the internet through mobile devices, more WordPress theme and plugin companies are focusing on responsive development, optimizing for readability and usability while taking in to consideration screen size, browser and device orientation. A few great examples of responsive themes include:
Responsive Layout Advertised in Features Sections
Most themes and plugins that offer a responsive design experience will proudly advertise this functionality under their features section on their website. They may also offer a demo for you to experience this functionality first hand. So make sure you keep an eye out, take your time and look around.