Please follow the way like below:
.selectParent {
width:120px;
overflow:hidden;
}
.selectParent select {
display: block;
width: 100%;
padding: 2px 25px 2px 2px;
border: none;
background: url("http://cdn1.iconfinder.com/data/icons/cc_mono_icon_set/blacks/16x16/br_down.png") right center no-repeat;
appearance: none;
-webkit-appearance: none;
-moz-appearance: none;
}
.selectParent.left select {
direction: rtl;
padding: 2px 2px 2px 25px;
background-position: left center;
}
/* for IE and Edge */
select::-ms-expand {
display: none;
}
<div class="selectParent">
<select>
<option value="1">Option 1</option>
<option value="2">Option 2</option>
</select>
</div>
<br />
<div class="selectParent left">
<select>
<option value="1">Option 1</option>
<option value="2">Option 2</option>
</select>
</div>