I find that sometimes it is the website that has some restrictions on iframes and references to external resources. But if that's not the issue, you might need to set the form as public if you don't want to have to be concerned about signing in. Use SetPermissions for this:

SetPermissions[obj, "Public"]

where obj is the link to your Cloud object (e.g. CloudObject["https://www.wolframcloud.com/objects/xxxx-xxxxx-xxxxx-xxxx-xxxxxxxxx"]). You also might want to check your HTML/CSS as well. Note that if you are using HTML5 on your website, the old way of specifying the properties of the iframe is depreciated.

Here is an example of deployed and embedding a web form:

CloudDeploy[FormFunction[{"size" -> "Number"}, Style["Hello, world", #size] &, "PNG"], Permissions -> "Public"]

Then take the URL that is returned, and put it into the iframe:

<iframe class="form" src="https://www.wolframcloud.com/objects/5cddd73e-5bb8-46f5-844d-c4417941383d"></iframe>

See the example on JSFiddle.

Hi Brian Lee, Sorry for the late reply, ...I have set the permission to Public and now it works fine. Now I have the EXPLORER plan, so I cannot check if it would work with the FREE plan? Anyhow, I plan to keep this plan, I guess this is the correct way. Thanks