The story of falcon stealing Soma and bringing it on earth is present in Rig-Veda. The story is not in one place but we can find the story in parts in various mantras from different mandalas.
I am providing answer from these mandalas RV 1.80.2 ,RV 1.93.6 ,RV 4.26.4 & 7 ,RV 4.27.3& 4 etc.
Here are the Sanskrit Mantras-:
स त्वामदद्वृषा मद: सोम: श्येनाभृत: सुत: ।
येना वृत्रं निरद्भो
जगन्थ वज्रिन्नोजसार्चत्रनु स्वराज्यम ।। RV 1.80.2 ।।
O Indra the holder of weapon Vajra. Your joy increased by the Soma
juice ( Which increases strength as well as intellect) brought by
falcon with great speed. Afterwards you killed the Vritra and
removed him from waters.
आन्यं दिवो मातरिश्वा जभारामथ्नादन्यं परि श्येनो अद्रे: ।
ब्रह्मणा वावृधानोरुं यज्ञाय चक्रथुरु लोकम् ।। RV 1.93.6
O Agni deva and Soma deva ,from you two Agni deva is brought here from
Dyu-Loka (Swarga , heaven) by "Maratishwa Vayu"for Bhrigu Rishi. And
Soma the second is forcefully brought from mountain top by a falcon.
प्र सु ष विभ्यो मरुतो विरस्तु प्र श्येन: शेनेभ्य अशुपत्वा ।
अचक्रया यत्स्वधया सुपर्णो हव्यं भरन्मनवे देवजु ष्टम् ।। RV
O Marud-Ganas you are more powerful and speedy with compared to Hawks.
The Soma which is offered to gods in yajnas as"Havya" is brought from "Swarga"(Heaven) by the bird (Hawk) of excellent wings with the
help of chariot without wheels , for the human beings (Prajapati
आदाय श्येनो अभरत्सोमं सहस्रं सवां अयुतं च साकम् ।
पुरान्धिरजहादरातीर्मदे सोमस्य मुरा अमुर:।। RV 4.26.7 ।।
Then the Shyen Bird (Hawk) took flight , with the aid of thousand
Yajnas. After that the Indra ,who has done many excellent good deeds
and a knowledgeable one killed many enemies with joy.
अव यच्छेयेनो अस्वनीदध द्योर्वि यद्यति वात ऊहु: पुरान्धिम्।
सृद्यदस्मा अव ह क्षिपज्जां कृशानुरस्ता मनसा भूरण्यन् ।। RV 4.27.3
While bringing the Soma from Dyuloka the falcon made a loud roar and
then the "Soma-Pala's" (Protector's of Soma) tried to take it away the
soma which increases the intellect , from him. After that the the
"Krishanu" prepared his Bow & sent forth a arrow upon the falcon.
ऋजिप्य इमिन्द्रावतो न भुज्युं श्येनो जभार बृहतो आधी ष्णो: ।
पतत्पतत्र्ययस्य पर्णमध यामनि प्रसितस्य तद्वे:।। RV 4.27.4
As the Ashwini Kumaras abducted "Bhujyu" from the place protected by
mighty Indra , in the same way the falcon which flew in straight path
stole the Soma from Dyuloka , protected by Indra. At that time from
the weapon's of "Krishanu"the falcon got injured and his one wing
प्र श्येनो मदिरमंशुमस्मै शिरो दासस्य नमुचेर्मथान । RV
Pleased by the Soma brought by falcon
Indra cut the head of wicked Namuchi
The brief story - The Soma juice was brought from mountain top.of Dyu-loka (Swarga, Heaven) by a falcon having very powerful wings. It was handed down to humans (prajapati manu) by him as offering in Yajnas. Indra and other Soma-Palas were guarding the soma over there , after stealing the soma juice the falcon with the aid of thousand yajnas flew from that place. The guardians of soma resisted to falcon stealing soma. One of the guards called "Krishanu" shot a arrow at the falcon and due to which one wing of the bird broke off .Afterwards Indra slew the Vritra and Namuchi by drinking this soma juice.
Note -:interestingly in the translation of Mandala 10 - Sukta 11-mantra 4 , we can see that this falcon is actually "Surya" the Sun god. Who is called as Suparna (with good wings).