I have a bootstrap card Which is used as a link.
Trying to wrap it with  changes all of the styling of the card.
You can put text-dark utility class to the element to have the same appearance.
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css">
<a href="">
  <div class="card text-dark" style="width: 15rem; display: inline-block">
    <img class="card-img-top" src="https://placeholdit.imgix.net/~text?txtsize=33&txt=318%C3%97180&w=318&h=180" alt="Card image cap">
    <div class="card-body">
      <h5 class="card-title">Wrapped with a tag</h5>
      <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
    </div>
  </div>
</a>Just add "cursor: pointer;" to your style
Try to add Display: Block to the link itself. Use your browsers Developer Tools (F12) and hover over the link to see if you need to add Height:auto perhaps.
Its because <a> tags has a default blue color from user agent browser.  Try to add a class to the link and set color:inherit to that class
a.custom-card,
a.custom-card:hover {
  color: inherit;
}<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css">
<div class="card" style="width: 15rem; display: inline-block">
  <img class="card-img-top" src="https://placeholdit.imgix.net/~text?txtsize=33&txt=318%C3%97180&w=318&h=180" alt="Card image cap">
  <div class="card-body">
    <h5 class="card-title">Normal card</h5>
    <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
  </div>
</div>
<a href="" class="custom-card">
  <div class="card" style="width: 15rem; display: inline-block">
    <img class="card-img-top" src="https://placeholdit.imgix.net/~text?txtsize=33&txt=318%C3%97180&w=318&h=180" alt="Card image cap">
    <div class="card-body">
      <h5 class="card-title">Wrapped with a tag</h5>
      <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
    </div>
  </div>
</a>bootstrap make it easy with Stretched link
<div class="card" style="width: 18rem;">
  <img src="..." class="card-img-top" alt="...">
  <div class="card-body">
    <h5 class="card-title">Card with stretched link</h5>
    <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
    <a href="#" class="btn btn-primary stretched-link">Go somewhere</a>
  </div>
</div>
If you are using Bootstrap 4.3 you don't have to wrap card with <a> tag, but instead put it inside card-body, and use stretched-link class. This is much cleaner way.
Visit https://getbootstrap.com/docs/4.3/utilities/stretched-link/ for more details.
If you can't use Bootstrap 4.3 this is styling for stretched-link class:
.stretched-link::after {
    position: absolute;
    top: 0;
    right: 0;
    bottom: 0;
    left: 0;
    z-index: 1;
    pointer-events: auto;
    content: "";
    background-color: rgba(0,0,0,0);
}
Here is the example:
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css">
  <div class="card" style="width: 15rem; display: inline-block">
<img class="card-img-top" src="https://placeholdit.imgix.net/~text?txtsize=33&txt=318%C3%97180&w=318&h=180" alt="Card image cap">
<div class="card-body">
  <h5 class="card-title">Normal card</h5>
  <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
</div>
  </div>
  <div class="card" style="width: 15rem; display: inline-block">
<img class="card-img-top" src="https://placeholdit.imgix.net/~text?txtsize=33&txt=318%C3%97180&w=318&h=180" alt="Card image cap">
<div class="card-body">
  <h5 class="card-title">Alternative</h5>
  <p class="card-text">Some quick example text to build on the card title and make up the bulk of the card's content.</p>
  <a href="#" class="stretched-link"></a>
</div>
  </div>