A button element can't use a href attribute. Use an A (anchor) element instead and style it to look like a button as you've just done.
Use the :hover :active pasuados to change the style when a user hovers or clicks the button.
.btn-blue {
  background-color: #00FFF0;
  border-radius: 12px;
  border: 1px transparent solid; /* transparent border */
  color: black;
  padding: 13px 30px; /* remove 2px as we are now using the border */
  text-align: center;
  text-decoration: none;
  display: inline-block;
  font-size: 12px;
  opacity: 0.6;
  cursor: pointer;
}
.btn-blue:hover
{
  opacity: 1;
  background-color: #00EEE0;
  border: 1px #99ccff solid;
}
.btn-blue:active
{
  background-color: #00CCC0;
  border: 1px #000000 solid;
}
<a class="btn-blue" href="#">Get The App</a>
 
 
Now simply replace some of my code above with whatever styles you want.
UPDATE:
If you need a button with a fixed height check this code:
.btn-blue {
  background-color: #00FFF0;
  border-radius: 12px;
  
  /* add a transparent border or use #00FFF0 for color */
  border: 1px transparent solid;
  
  /* Allows us to include the padding and border in an element's total width and height. */
  box-sizing: border-box;
  
  color: black;
  
  /* remove the top and bottom padding, we don't need them */
  padding: 0px 30px;
  
  text-align: center;
  text-decoration: none;
  display: inline-block;
  font-size: 12px;
  
  font-family: Helvetica, Arial;
  
  /* Use this to set a fixed height so the height won't changes */
  height: 35px;
  
  /* Set to same as height so the text is centred in the middle. You can change the font-size or family without the box getting bigger */
  line-height: 35px;
  
  /* So that the box doesn't shrink or expand if the font-size changes on hover like in this example. */
  min-width: 150px;
  
  opacity: 0.6;
  cursor: pointer;
}
.btn-blue:hover
{
  font-size: 14px;
  font-weight: bold;
  opacity: 1;
  background-color: #00EEE0;
  border: 1px #99ccff solid;
}
.btn-blue:active
{
  background-color: #00CCC0;
  border: 1px #000000 solid;
}
<a class="btn-blue" href="#">Get The App</a>