Result

css

#box {
  display: flex;
  align-items: center;
  justify-content: center;
  width: 300px;
  height: 100px;
  color: white;
}
.gradient-border {/*変数設定*/
  --borderWidth: 3px;
  background: #1D1F20;
  position: relative;
  border-radius: var(--borderWidth);
}
.gradient-border:after {/*グラデーション設定。位置は先ほどの変数を代入してclacで計算*/
  content: '';
  position: absolute;
  top: calc(-1 * var(--borderWidth));
  left: calc(-1 * var(--borderWidth));
  height: calc(100% + var(--borderWidth) * 2);
  width: calc(100% + var(--borderWidth) * 2);
  background: linear-gradient(60deg, #f79533, #f37055, #ef4e7b, #a166ab, #5073b8, #1098ad, #07b39b, #6fba82);
  border-radius: calc(2 * var(--borderWidth));
  z-index: -1;
  animation: animatedgradient 3s ease alternate infinite;
  background-size: 300% 300%;
}

@keyframes animatedgradient {/*アニメーション設定*/
	0% {
		background-position: 0% 50%;
	}
	50% {
		background-position: 100% 50%;
	}
	100% {
		background-position: 0% 50%;
	}
}

html

<div class="gradient-border" id="box">foo</div>

ca i use

via

Animated CSS Gradient Border