Feeling awkward can make you think "I am simply bad at this, and I always will be," instead of "that one moment went badly." I have spent more than ten years coaching people that described themselves exactly that way. The ones that improved did it by fixing a couple of ordinary habits, without trying to become smooth or put on a personality, and the awkwardness faded on its own.
So before you accept "awkward" as a permanent fact about yourself, look at what is actually causing the feeling. It is less mysterious than it seems at two in the morning, and far more fixable.
Awkwardness is mostly a timing problem
Most awkward moments come down to timing. You answer a little late, get personal before you know someone well enough, or miss the cue that a conversation is wrapping up and keep it going too long. Each of those is a matter of calibration, and calibration is a skill that improves with practice.
Your attention is on yourself
Underneath a lot of awkwardness is a habit that is hard to notice in yourself. While you are talking to someone, part of your attention is on how you are coming across: "Do I sound weird? Was that too much? What do I say next?" That split attention causes most of the trouble, because you cannot fully watch yourself and fully pay attention to the other person at the same time. Watching yourself is what leaves you a little behind and a little stiff.
You might be thinking, "Fine, so I need more confidence." Confidence helps, but you cannot simply decide to feel confident. What you can do, starting today, is move your attention off yourself and onto the other person. When you are really interested in what they are saying, there is not much attention left over for watching yourself. It is very hard to be curious about someone and self-conscious at the same moment.
Warmth beats impressiveness
When we feel awkward, the instinct is to make up for it by trying to be funnier or smarter. The trouble is that trying to impress raises the stakes of the interaction, and higher stakes make everyone tenser, you most of all.
Warmth does the opposite. Being friendly, relaxed and glad to talk to the person in front of you puts everyone at ease, and people forgive awkwardness from someone that is obviously kind. You do not need to be smooth, and being warm is much easier to learn.
Learn the recovery move
Everyone has clunky moments, like answering a question you misheard or blanking on a name. Socially comfortable people have just as many of these as you do, but they do not try to hide them.
If you mention a clunky moment lightly, it is over in two seconds. If you lose your train of thought, say so with a small smile: "Sorry, total brain lag, say that again?" If you blank on a name, simply ask, "What was your name again?" Even people that are great with names forget them seconds after hearing them. It is the clunky moment you scramble to cover up that lingers.
Stop replaying awkward moments
One habit creates more awkwardness than any other: replaying. That means lying awake going over an embarrassing moment from three years ago, or imagining a disaster that has not even happened. Every time you do it, you teach yourself to treat ordinary conversation as dangerous, which makes you tenser next time and more likely to stumble, which gives you something new to replay.
You stop it in the moment. If you catch yourself replaying, name it to yourself ("I am doing the thing again") and put your attention on something real in front of you, like the person or what is being said. If the memory keeps coming back, let it be there without arguing with it, and bring your attention back each time. You do not have to win an argument with the memory, only stop rehearsing it.
Awkwardness is a set of habits
None of this requires changing your personality. Work on your timing, put your attention on the other person, lead with warmth, recover lightly from clunky moments, and stop replaying old ones. Each of these is a habit, and habits improve with practice the same way a jump shot does: clumsy at first, then automatic. You get to keep every bit of who you are.
Ease is a skill, and skills can be taught
My Social Skills Mastery course takes the mechanics of feeling at ease and breaks them into pieces you can practice on purpose, instead of waiting around for them to click on their own. If you'd rather talk it through with a person first, a free call is a good place to start.