final.css

.date-picker { position: relative; width:250px; }

.date-picker .date-icon {
   position:absolute;
   top:15px;
   right:-10px;
}

position_absolute.css

.date-picker .date-icon {
   position:absolute;
   top:0;
   right:0;
}

position_relative.css

.date-picker { position: relative; width:250px; }

.date-picker .date-icon {
   position:absolute;
   top:0;
   right:0;
}

sample.html

<div>
    <h6>Example:</h6>
    
    <div class="date-picker">
        <input type="text" placeholder="TextBox with an Icon" class="date-input">
        <a href="#" onclick="alert ('clicked');" class="date-icon">
            <img src="http://s3.amazonaws.com/wimgo/images/wimgo-search-date-popup-icon.gif" alt="">
        </a>
    </div>
</div>