How can I integrate the Web SDK in a Wordpress website?

This implementation actually depends on the customization your WordPress template allows. Branch does not have a direct WordPress integration so you would need to inject JS code in the tag.

You can add the following code in the <head> tag:

// load Branch
(function(b,r,a,n,c,h,_,s,d,k){if(!b[n]||!b[n]._q){for(;s<_.length;)c(h,_[s++]);d=r.createElement(a);d.async=1;d.src="";k=r.getElementsByTagName(a)[0];k.parentNode.insertBefore(d,k);b[n]=h}})(window,document,"script","branch",function(b,r){b[r]=function(){b._q.push([r,arguments])}},{_q:[],_v:1},"addListener applyCode autoAppIndex banner closeBanner closeJourney creditHistory credits data deepview deepviewCta first getCode init link logout redeem referrals removeListener sendSMS setBranchViewData setIdentity track validateCode trackCommerceEvent logEvent disableTracking".split(" "), 0);
// init Branch

Once you are able to add the above code to the tag, you should be able to use Branch Web SDK functions.