There are several methods to add “Attach File” control in the new form.
Method 1: Add the following code using Content Editor web part or Script Editor web part in the NewForm.aspx page. When clicking the hyperlink “browse”, OOTB “Attach File” featurewill be triggered and user will be able to select a file in the current site and insert into the current item as an attachment.
<script type="text/javascript">
function AttachFile()
{
SP.Ribbon.PageManager.get_instance().executeRootCommand("Ribbon.ListForm.Edit.Actions.AttachFile", null, null, null);
}
</script>
<a onclick='javascript:AttachFile();'>browse</a>
method 2: Open the NewForm.aspx using SharePoint Designer. Place the below code where you would like to insert the Attachment Field.
<tr>
<td width="190px" valign="top" class="ms-formlabel">
<h3 class="ms-standardheader">
<nobr>Attach Files</nobr>
</h3>
</td>
<td valign="top" class="ms-formbody" id="attachmentsOnClient" style="width: 434px">
<span dir="ltr">
<input type="file" name="fileupload0" id="onetidIOFile" size="56" title="Name"> </input>
</span>
</td>
<td width="100px" valign="top" class="ms-formbody">
<input name="Button1" type="button" value="Attach" onclick='OkAttach()' style="width: 6em;
height: 1.7em" />
<span id="idSpace"></span>
</td>
</tr>
Refer to: Add attachment button to a custom new form SharePoint 2013
Method 3: Customize the new form using the InfoPath. Click on “Customize Form” on the ribbon under List tab to customize the list form using InfoPath. Include Attachment field in the form.