I am currently building a website which requires buttons to have a slant on the left hand side of the button. The website is responsive and the button requires rounded corners too. I am trying to avoid using background images too.
Would someone be able to show me a solution to this? Ignore the icon on the button, I am able to do this. I just need the slanted side.

Sample jsfiddle
body {
  background: lightblue;
  font-family: sans-serif;
}
div {
  background: purple;
  width: 200px;
  padding: 30px;
  border: 3px solid white;
  color: white;
}<div>Some Text</div>Note: I am adding a separate answer because though the answers that I linked in comment seem to give a solution, this one is a bit more complex due to the presence of border also along with the border-radius.
The shape can be created by using the following parts:
I have also added a hover effect to the snippet to demonstrate the responsive nature of the shape.
.outer {
  position: relative;
  height: 75px;
  width: 300px;
  text-align: center;
  line-height: 75px;
  color: white;
  text-transform: uppercase;
}
.outer:before,
.outer:after {
  position: absolute;
  content: '';
  top: 0px;
  height: 100%;
  width: 55%;
  background: purple;
  border: 2px solid white;
  border-left-width: 3px;
  z-index: -1;
}
.outer:before {
  left: 0px;
  border-radius: 20px;
  border-right: none;
  transform: skew(20deg);
  transform-origin: top left;
}
.outer:after {
  right: 0px;
  border-top-right-radius: 20px;
  border-bottom-right-radius: 20px;
  border-left: none;
}
/* Just for demo of responsive nature */
.outer{
  transition: all 1s;
}
.outer:hover{
  height: 100px;
  width: 400px;
  line-height: 100px;
}
body{
  background: lightblue;
}<div class='outer'>
  Call me back
</div>Advantage:
In the below snippet, I have given each component a different color to visually illustrate how the shape is achieved:
.outer {
  position: relative;
  height: 75px;
  width: 300px;
  text-align: center;
  line-height: 75px;
  color: white;
  text-transform: uppercase;
}
.outer:before,
.outer:after {
  position: absolute;
  content: '';
  top: 0px;
  height: 100%;
  width: 55%;
  background: purple;
  border: 2px solid white;
  border-left-width: 3px;
  z-index: -1;
}
.outer:before {
  left: 0px;
  border-radius: 20px;
  border-right: none;
  transform: skew(20deg);
  transform-origin: top left;
  background: seagreen;
  border-color: red;
}
.outer:after {
  right: 0px;
  border-top-right-radius: 20px;
  border-bottom-right-radius: 20px;
  border-left: none;
  background: yellowgreen;
  border-color: maroon;
}
/* Just for demo of responsive nature */
.outer{
  transition: all 1s;
}
.outer:hover{
  height: 100px;
  width: 400px;
  line-height: 100px;
}
body{
  background: lightblue;
}<div class='outer'>
  Call me back
</div>Yes You can do using an white overlay using css-pseudo element before or after like this
.slantButton {
  position: relative;
  background-color: #8D3F81;
  border: 1px solid transparent;
  border-radius: 5px 5px 5px 20px;
  color: #fff;
  padding: 10px 20px;
  text-transform: uppercase;
  font-size: 18px;
  cursor: pointer;
  outline: 0;
}
.slantButton:before {
  content: '';
  position: absolute;
  top: 0;
  left: -5px;
  width: 0;
  height: 0;
  border-bottom: 42px solid #fff;
  border-right: 16px solid transparent;
}<button class="slantButton">Call Me Back</button>I have applied different border radius to bottom left corner using
border-radius: 5px 5px 5px 20px;
Then using css triangle in pseudo element. Made one white overlay of triangle and made slant edge as you suggested
    .slantButton {
      position: relative;
      background-color: #8D3F81;
      border: 1px solid transparent;
      border-radius: 5px 5px 5px 20px;
      color: #fff;
      padding: 10px 20px;
      text-transform: uppercase;
      font-size: 18px;
      cursor: pointer;
      outline: 0;
    }
    .slantButton:before {
      content: '';
      position: absolute;
      top: 0;
      left: -5px;
      width: 0;
      height: 0;
      border-bottom: 42px solid rgba(0,0,0,0.5);
      border-right: 16px solid transparent;
    }<button class="slantButton">Call Me Back</button>This is also possible using CSS border-radius' by setting multiple values.
This does have a bit more curvature than your example image but it is much cleaner and doesn't require extra elements or pseudo elements.
body {
  background: lightblue;
  font-family: sans-serif;
}
div {
  background: purple;
  width: 200px;
  padding: 30px;
  border: 3px solid white;
  border-radius: 15px;
  border-bottom-left-radius: 50px 150px;
  color: white;
}<div>Some Text</div>If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With