What is the relationship between yoga and orthodox Hinduism?

It has been argued that Sankhya (enumeration, or ‘count’) and Yoga may have had their earliest origins in the Indus valley civilization. Yoga refers to a separate philosophical school or darshana, but it is also used in a wider sense to describe different methods of self-control and meditation in Hinduism.

The Yoga school of thought relies on Sankhya metaphysics and uses as its basic text the Yoga Sutra of Patanjali, dating from teh 2nd century before Christ. Yoga differs from Sankhya in that it emphasises specific practices for the attainment of liberation and introduces the Lord, Ishvara, as an object of devotion. He is presented as a specially exalted sould which has never been enmeshed in matter, a methodical help and meditational focus for the seeker. The final goal of Yoga, however, is not union with him but isolation of the soul.

The practices of Yoga may be very ancient - a figure seated cross-legged can be seen on some of the Mohenjo Daro seals from the Indus valley. The Yoga school has developed carefully graded phsical and spiritual exercises which in modified form have become part of many schools of Hinduism.

“Is yoga an orthodox division of Hinduism from the beginning?”.
Before we begin to answer this question, we need to understand what Hinduism means. The word Hinduism can be looked at from two different points of view. In the Indian thought, the Vedas are considered to be the source of all knowledge. They are called “Apaurusheya” (not created by humans) or “shruti” (knowledge that his ‘heard’ by the rishis in their deep meditation). The essence of the Vedas has been made available in the Upanishads. If by Hinduism we understand the knowledge that is in the Upnishads, then I think it is fair to say that Yoga is an outgrowth of Hinduism. However, the common practice of Hinduism today is based on a belief system and involves a lot of rituals which are based on the teachings from the Puranas. Thus we have sects like Vaishvanites, Shaivites etc. As far as I know these systems have evolved later than the original Yoga philosophy. Here by Yoga we mean one of the six “darshanas” or the six schools of Indian philosophy (Nyaya, Vaisheshika, Yoga. Sankhya, Mimansa, Vedanta). In this case I would say that your second statement, “Or yoga originally had nothing to do with Hinduism, but has been absorbed in Hinduism later?” is more apt. However “nothing to do with Hinduism” is rather too strong because both yoga and Puranas are subsequent to and based upon the knowledge in the Vedas. So I would say that it is possible to practice yoga without any involvement with the ritual side of Hinduism. However, it must be kept in mind that many of the concepts in yoga (for example ‘karma’ and ‘reincarnation’ etc) are common to Hinduism as well.