You can use Delegate Controls to add jQuery to each page of SharePoint without modifying it.There are multiple Delegate Controls available OOB in SharePoint Master page like the one below. You can over ride them using a webpart to inject jQuery into master page without modifying it.
<SharePoint:DelegateControl runat="server"
ControlId="AdditionalPageHead"
AllowMultipleControls="true"/>
Delegate controls are particularly useful in SharePoint when you want to add functionality to all pages within your site without changing the master page. For example, if you want to add an external JavaScript library (such as JQuery) to every page, you can do this easily by registering a delegate control. An example of this approach can be seen here
You can also refer these examples :
Example 1
Example 2