Yes, objective human morality can come from holy scripture. Since God is the only objective definer of human morality that has ever, and will ever, exist, and scripture is His Word, scripture does teach objective human morality. Objective morality can't come from anywhere else, or it isn't objective. God is the ultimate standard.
I think that holy scripture, or religion itself has shaped everyone's thought on the planet. Objectivity is really now based on the norm of society, and that norm has come from religion (whatever it might be). I don't think humans on earth today have even come close to thinking more objectively, because of religion.
The idea of, you have to think this way, because God said it so in this verse, is oh so true. Our whole society is victim to this, and we are barely starting to think outside of the box.
I think it can, and it has for ages. Much of our law coincide with the scriptures. For instance, the ten commandments have many overlapping principles. I think the bible puts a large focus on every man being equal before god and being bound to the same laws. I like to think the scripture cannot be neglected on the topic of human morality.
What is objective morality? How objective can we truly be regarding morality? Various holy scriptures (and other philosophical and spiritual texts) offer wisdom to mankind that is generally considered good and wise. Most reading this question only seem to think of the Bible or Koran. I think of these, the Tai De Ching and many more. There are many subjective, and just plain wrong verses and tenets in religion. However, there is also much good to be found in all religions I have studied thus far. I have found that there are many (what I consider to be) objective moral truths such as "do not murder" in scriptures.
Objective reasoning cannot be achieved by deriving the answers from scripture. Scriptures around the world disagree with how to handle moral dilemmas, suggesting that they must be subjective, or else they'd all agree with one another. Scripture itself contains very few objective morals, making it incredibly difficult to imagine being successful at actually instilling them.
Allow me to use the Euthyphro Dilemma to illustrate. Let us say that some action is good, and it is also 'known', for the purpose of this argument, that this action is also commanded by God. Is the act good because it is commanded by God, or does God command the act because it is good? If the former, then the 'morality' that is apparently being used to demonstrate is nothing more than a fallacious appeal to higher authority, and thus inherently meaningless. If the latter, then the action is good completely independent to the 'will of God', and the act would continue being good even if God ceased to 'command' it.
In essence, whether or not an arbitrary being/book 'commands' some specific act has no bearing on the morality of said act. It would theoretically be possible for God/the bible to 'command' the slaughter of all left-handed individuals. This act is still necessarily immoral, regardless of the command, or what it says in 'holy scripture'.
Even going without this argument, religious 'scripture' in the real world is authored entirely by the hands of humans, and is not necessarily indicative of the will of God, if indeed he exists. Thus, the statement that 'morality' could possibly be factored down to 'it says so in that book I read' is completely ridiculous.
From whence comes [morality]? Is it pleasing to the gods because of their whim, or is there some greater nature of gods by which it becomes pleasing to them? If it is the former, it is subjective to the god. If it is the latter, it does not come from the gods but from elsewhere. If it is from elsewhere, then it is merely incidentally IN, rather than FROM the "holy" scripture.
The main theological idea is that god is moral and never immoral, so all of his actions are moral. Some point to the 10 commandments and assert that our own laws follow much of it but we do not find it objectively moral to punish those who don't practice the Sabbath, nor do we find those people to be immoral. Furthermore the commandment against killing, we find in 2Sam 12, God kills a child because he is mad at the parent for the parents action towards another adult. Is it objectively moral to kill children for the actions of the parent?
Now perhaps some one may suggest some sort cherry picking to suit the times but then one is subjectively pickling which parts to use in support of some other morality and using the bible to legitimize it.
Tough question for sure, but I'd be inclined to say no. You're being guided in a specific way if you're following a specific line of scripture, I think that makes it hard to argue it's objective and looking at the bigger picture. A more religious person would likely have a completely different answer.