If you choose the Arcane bloodline then no, there are no bloodline powers that the Halfling favoured class option can apply to. But this doesn't mean that you don't gain any bonuses for sorcerer being your favoured class, you just fall back to the standard options. You can only chose the +1 hit point or skill rank per level.

If you wanted to use the Halfling's favoured class option then you would have to choose a different blood line, one with a power that meets the requirements, such as Celestial (Heavenly Fire power).

Using a spell-like ability is not casting a spell

The elemental bloodline special ability elemental ray says

Elemental Ray (Sp): Starting at 1st level, you can unleash an elemental ray as a standard action, targeting any foe within 30 feet as a ranged touch attack. This ray deals 1d6 points of damage of your energy type + 1 for every two sorcerer levels you possess. You can use this ability a number of times per day equal to 3 + your Charisma modifier.

The special ability elemental ray is a spell-like ability and isn't a spell, and using the special ability elemental ray isn't casting a spell. The orc the question describes deals 1d6+1 points of fire damage with the spell-like ability elemental ray.

How to compute the spell level of this spell-like ability is covered by the FAQ… and the FAQ has several rulings that explain how spell-like abilities differ from spells (such as here, here, and here).

Each special ability in turn

• The orc bloodline sorcerer arcana says, "Whenever you cast a spell that deals damage, that spell deals +1 point of damage per die rolled."
• The wildblooded archetype's primal elemental bloodline sorcerer arcana says, "Whenever you cast a spell with an energy descriptor that matches your elemental bloodline’s energy type, that spell deals +1 point of damage per die rolled."
• The orc sorcerer favored class ability says, "Add +1/2 point of fire damage to sorcerer spells cast that deal fire damage."

None of these special abilities function in conjunction with using a spell-like ability. I recommend the casting the spell burning hands until the spell scorching ray becomes available.

Further insight and explanation is available from the question Are Spell-Like Abilities Actually Spells? and Can "Basic Magic" be used with Arcane Strike on an (Evolved) Companion?

Note: The FAQ clarified in Oct. 2013 that the sorcerer archetypes crossblooded and wildblooded can't be combined. This thread, for those interested, debates that ruling at length.

The FAQ in Nov. 2013 ruled that the feat Augment Summoning applies—uniquely—to spell-like abilities as well as spells, despite the feat's description specifying only spells.